We moved over a few months ago. I sincerely regret that I was intimidated by Argos (large catalog, reminiscent of old JC Penny or Sears catalog ordering stores--remember those? in the US) and did not check out their very good online features. In particular, they have reviews of the items they carry and that is helpful when buying electronics--which is the scary stuff you pretty much have no choice but to buy again.
So, I did the Wilkinson/TK Maxx route, but if I did it all over again, I'd go with Argos.co.uk and feel more confident as I think the reviews on Argos are helpful. In particular, I would look at TVs there first and stuff like clock radios... TK Maxx is (like the US TJ Maxx) where department store-rejects go to finally sell. It's pretty good, but, I think a few items we obtained from there were lower quality than they should have been--ie: the pillows we bought are becoming clumpy, and the non-stick pan has the non-stick material coming up. Looking back, I should have just paid £5 more at argos for such items. Wilkinsons is probably best compared to the U.S. Walgreens (which went out of business here recently). This is a place you pop into for the random-need-it-now purchase, like brillo pads, light bulbs, and school supplies. They do have a few home-decor items. But, they are of varying qualities and not wholly dependable.
I emphasize the dependability factor, because if you are moving here for the long haul,like we did, then you need to have a different perspective in your purchasing than the buy-it-and-don't-care-if it-is-in-the-trash-in-6 months attitude. I also say this becuase I was totally stupid and now own a number of truly crappy items. And, whern you have a whole lot of items that are falling apart--you don't feel like you're at home.
Otherwise, because the economy sucks, a LOT of stores are going out of business--particularly home decor shops. So, lamps, curtains, and the like are worth hitting the pavement for--because there are bargains to be had in that area.
I also found that A LOT of women are selling their rarely/unused household goods through the netmums website. I find that amidst the resale of baby/child goods it is also a haven for wedding-present-resale items. I got a nearly new blender and a crock pot for about £5 each through that. I scan ther info regularly.
Best of luck!