Sweet peppers are varieties of chilli pepper (specifically capsicum annuum) that have had the hotness bred out of them (by the Dutch). Sweet peppers are grown in practically the same way as hot chilli peppers. If you want detailed intelligence on how to grow peppers in Britain you could check out a UK-based chilli forum such as http://www.chillisgalore.co.uk/phpBB2/index.php - the info will apply pretty much the same to your sweet peppers. Also http://www.thechileman.org/guide_home.php has basic growing guides for peppers, written by a man from Darlington.
You will discover that UK home pepper growers commonly sow their peppers as early as Feb, in order to have the plant sufficiently advanced to fruit when the warm weather comes, taking into account the low light conditions here in the UK. To have a 7" plant by now is nothing unusual. They are a bit larger than mine, which are in the, er, lounge, as I don't have a greenhouse.