I'm living in Belfast and have attempted to grow a few herbs myself, some with success and some without a lot. I started off by sowing seeds for everything to make sure it would work well and the thyme and parsley are doing great, however the basil is looking a little sad. It could be a number of things: that I have it outside and it's been raining ALL the time with little sun, or the fact that it's not been that warm. So I may move the healthier basil plants back inside so at least the temperature will be better. The thyme, on the other hand has been goign crazy. I sowed a lot in a flat tray and, being the humane person who hates to thrown things out, left the smaller plants in the tray outside while I potted the bigger ones in an east facing window that gets loads of sun. THey're both doing about the same, so you may have more success with thyme than anything.
From my experience with buying pre-grown plants, re-potting almost always does a world of difference, ESPECIALLY with basil because it tends to get root-bound in the pot. If you can lift the plant and the soil out of the pot in one fell swoop, then YES you really need to get it into a bigger pot. Don't be afraid to loosen up the roots and get them stimulated to grow more, you won't kill the plant unless you actually remove big chunks of root.