Martin,
Try and get hold of a potato called Swift, this is very fast growing about 10 weeks.
If you have a green house get some pots about the size of the black flower buckets already mentioned. Put two seed potato's in each bucket which should be about 1/3 full of compost making sure the seeds are covered.
When the greenery starts to show gradually fill the bucket with compost, making sure you always leave the greenery above ground so to speak. Keep well watered and fed I use Miracle grow.
At ten weeks carefully pull the plant out of the pot and have a look at what you have got. If not quite ready slide plant back into pot and leave a futher 2 weeks.
Each pot should keep you in new potato's for about a week.
I would normally start this about mid Feb so my extra earlies are ready at the same time as the Jersey Royals are at their most expensive.
Colin H.