A friend asked me last week what kind of fire extinguisher I had in my garden office/shed. When I said I didn't have one, he pointed out that since it was built of wood, was full of books, paper and often rather hot electrical equipment, and was next to a wooden fence leading directly to my house, perhaps I should invest in one before bonfire night next year.
There's a real dearth of information about fires and home offices so I've culled the following from various sources, but it goes without saying that you should contact your local fire station for expert advice before buying anything.
Extinguishers are rated as A, B, and C and if you put out a fire on your desk with the wrong one, you could destroy your computer. So what most of us are looking for is a Type C: this one contains halon (or sometimes some other kind of dry chemical) which is non-corrosive so won't destroy your laptop, although the bad news is that it's not great for the ozone layer and can be toxic so be carefuly if you use it in a confined space. Also, big is not necessarily best. Extinguishers are heavy brutes and a smaller one might be easier for you to use in an emergency.
Pictured is an example, a Kidde Home/Office Fire Extinguisher FA460 which should do the job nicely, though it is quite big. For more information you could also try AGF Fire Protection Ltd.