Hi Holly,
The actual wiring connections are easy. The fiddly part is figuring out the best way to mount a replacement lampholder and thread the cord through the lamp base, which depends very much upon the design, obviously.
The holders on table lamps are generally mounted via a threaded boss at their base, so as long as you can find some way to adapt an existing bracket or mount a new one it's not too difficult. Depending upon the origin of the lamps and the threads used, you might even be able to just screw a British replacement straight on, otherwise it will be a case of changing the mounting nipple as well for one with the correct threads.
Either way, it's not that difficult and if you don't mind spending a little time to do the job yourself, it's relatively cheap. A replacement lampholder, cord, and plug shouldn't cost more than £5 ($10), even at High Street prices.
The DIY chains such as B&Q (like Home Depot), Wilkinsons etc. sometimes carry full lamp wiring kits, but a little backstreet electrical shop is often a better candidate for carrying a wider selection of the "extras," like mounting nuts and nipples, brackets, and so on.
You might like to have a look at this site to see a selection of the types of mounting hardware and lampholders available:
http://www.s-lilley.co.uk/site/homeframe.htmAll of this is assuming you have just a regular table lamp. If they're dimming types or those fancy electronically controlled types where you just touch the metal base to switch on and off, then conversion is almost certainly not worthwhile, unless you want to forego all the fancy stuff and just convert them to a simple lamp with on/off switch in the cord or on the holder.
Danke
Bitte!