'but of similar dimensions to the largest weather-related disasters and earthquakes'
Unfortunately the overall impact of a nuclear detonation will be a lot worse due to the long and medium term impact of the exposure to radiation, including cancers and birth defects. The fallout area will be unusable for a long period of time. Natural disaster are more time limited, with immediate deaths, injuries and with fewer long term consequences.

Perhaps the biggest threat these devices pose is not the actual number of casualties that would result from their detonation, it is the threat they are capable of posing.
Give any terrorist organisation a few of these, such as might happen if someone breaks the padlock on the garden shed in which are stored a number of battlefield nuclear weapons, and they could have any nation belly up within a few short weeks. All that they would need to do is simply detonate them randomly one at a time without warning in various centres of population. A few days between some, a week or so between others with perhaps even a month on one occasion, just to give some false hope to the populace that the nightmare was over.
How long then before those living in any population centre fled to the hills? How long then before the food ran out? How long then before the population became feral, scavenging for food, searching for uncontaminated water, etc.? Imagine such a scenario in a nation personally armed to the teeth. The military would have no identifiable target to aim at, and anyway, it would soon be severely diminished due to troops deserting in order to defend their kith and kin. The struggle to return to what might be called civilisation would take many years, during which time any position in world governance would be long gone, probably never to return.
One has always to try and spot the politics in such press release items as this one. Do the authorities know something we don't? My personal test as to whether terrorists have managed to obtain nuclear weapons is if, when I turn on the radio first thing on the first of January, the programme is not discussing the destruction of New York at the instant the Time Square countdown to the new year reached zero. This is closely matched by the lack of the destruction of Washington during the State of the Union address to both houses. The first would be symbolic, New York being the home of capitalism; the latter much more effective by removing the governance, leaving the chicken headless, so to speak.
Any talk of a nation's ability to launch nuclear tipped missiles is a diversion. It would be folly to do so, seeing as the point of origin would be known. In contrast, you cannot put the pieces of an atom bomb back together in order to obtain clues as to its manufacture. The scary thing is that there could already be in situ such devices, their electronic timers counting inexorably towards a fate that none of us would wish on our worst enemy.

If you see a large flash, hit the ground and cover your ears tight to absorb some of the concussion a second later.
Radiation enters mostly through the respiratory tract and open wounds. As such, the following would be handy to stash at home or work in some kind of solid box: 1. iodine tablets 2. better then p100 class particulate respirator with spare filters to last at least a few days (each filter good for ~4-8 hrs continuous operation depending on fitness level and exertion). 2. painter's disposable suit 3-4 of to change daily 3. first aid kit. 4. 10L of water bottles in a backpack.
If you survive the blast, find these items, pop the pills, patch and wash your wounds immediately then put on the suit and mask.
These things together costing less then $200 will put you further ahead of the curve.

The article forgets to mention the subway. It is probably the best shelter in downtown NY and its tunnels allow you to move out of the danger zone while being pretty well protected from the fallout. So if you have a subway in your city, you are lucky... The article also forgets to mention that concrete buildings are a very good way to block the blast and the heat. The more tall buildings made from concrete and steel a city has, the smaller the radius of destruction. Because of this, the higher yield bombs are generally exploded higher above ground. This also means that simply putting a 300kt bomb on top of the empire state building will not automatically result in that much more damage compared to the lower yield bomb (and the effect generally does not scale linearly). I also want to point out to Brian that birth defects and long term cancer is generally exaggerated by popular media. I suggest to read up on the so called "life span study" about the survivors of Hiroshima and Nagasaki. If you survive the initial blast (without severe injuries or maximum exposure) and get treatment right away, your life span will be minimally reduced. Birth defects as a result of the radiation are rare. Another good advice that was not mentioned here is to protect your mouth with a makeshift filter of sorts to avoid inhalation of radioactive particles. External exposure to radiation is a lot less damaging than internal exposure. So avoid ingesting or inhaling radioactive particles and try protecting your eyes with glasses. A full face gasmask would probably be ideal, but most people don't have access to that.

Mel, get a grip. This article is based on a paper submitted to the Royal Society last October. If the government has new information about a threat, it is not imminent.
Do the authorities know something you don't? Yes. They know nuclear weapons are not stored in garden sheds. And they do know how to analyze a nuclear explosion to trace the fissile material back to the source. If it was a stolen weapon, it would still not mean they would know who set it off, but if it were terrorists, they usually take credit. So the response would probably not be a nuclear missile, but more likely an air strike or a Seal team.
Read Cresson Kearny's 'Nuclear War Survival Skills', stockpile food and ammo and some old Jerry Ahern 'Survivalist' paperbacks in your bunker and try not to worry.

@Mbadgero
Whilst nuclear weapons are not stored in garden sheds any longer, when the Cold War came to an end it was discovered that the storage of Soviet battlefield nuclear weapons was as good as their being stored in sheds with padlocks under the guard of a disillusioned soldiers who were unpaid for many weeks at a time. How much do you think a battlefield nuclear weapon would have fetched on the black market?
Regarding your point that terrorists "usually take credit", "usually" is no guarantee that they always will, and anyhow, going back to the days that the U.K. was under threat from the IRA, where exactly would we have pointed our 'deterrent'? Belfast maybe? Dublin possibly? I think you will find that it isn't me who needs to get a grip. We have missed a glorious opportunity to make the world a safer place following the end of the Cold War thanks to complacency. Now where are we? Not in the place we should be in if we didn't have such a bunch of clowns for politicians, that's were.

I recommend what the government had us do in grade school air raid drills in the early 50's. Crouch under your desk and kiss your little ass goodbye.

Really? I have just a couple of question... what are you going to breath, how long do you expect you food stuffs to last? Not to mention how will you protect yourself from those who want what you have and will eventually get it. Also even if you do survive, then what and so what? How pleasant do you think it would be being the only few left on a planet or continent to start civilization all over? No thanks... I would rather be at ground zero so as not to have to waste my time with all these fluffy thought of a great outcome. Because you're going to die one way or the other and if you would rather be in a confined space watching your limited supply of everything deminish as the inevitable comes about more power too you.

The suggestion for retreat is made interesting as in, trapped in your car, stuck in a traffic jam... When a hurricane approached Houston, it was a spectacular nightmare of epic proportions of fleeing Houstonians.
If the area is not on fire, and many areas will be burning, bunkering down in the center of your house is an option. Plug up doorways, pull heavy objects, even books near this center retreat area... and take that Iodine! Make shift masks out of wet cloth can help. And take at least some time to bring in with you as many gallons of water as you can as the lack of water will kill you faster than many can think. As fat Americans we carry our food, water, not so. Later you can think of retreating past all of the dead and dying stuck on the road. Sound like movie material...

I have a book in my library called "Forecast 2000", by joseph pulitzer jr. published in 1984. It mentions a possible attack from "terrorists" in the form of a threat of detonation of a nuclear device from the Empire State Building...how prescient.
On the other hand, what advice could we have given to the residents of Hiroshima, Nagasaki or Faludjah, Iraq?
This is a complicated and risky new world we're living in. There are many things done by state governments that can be counter-productive in the name of security. So we go on living in spite of it all, because having a dreadful existence is no way to live...
Just make sure your pantry is full and you have at least a rudimentary supply of necessities.