Have a llook at DSLZone for a comparison of ISPs and their ratings (it also explains various things in a helpful manner, with links to the ISPs it rates.)
I also wanted to avoid LLU, NannyNick, and have gone with ADSL24 (changing from Pipex). I went for their fixed-speed package of 2mbs (all my exchange can manage) with a 30gig peak d/l cap a month - plenty for my needs, we will barely use 6 gb this month, though that will change at Xmas when my DDs are home and we will then have 3 pcs and 2 lappies on the go. However, there's also an allowance of 300 gb OFF-peak (1opm-8am and all weekend) so I'll encourage them to do most of their music downloads then - though I still think 30 gb is plenty for normal use, unless you do torrents.
I do recommend ADSL24, the contract is only for one month and as you can see from DSLZone they are currently rated one of the top ISPs in the UK. Haven't had any problems and the changeover was very smooth. They do cap off-peak speeds to 2mbs though - no problem for me as it's all I can get - but might annoy you if you get more all day and then come down at nights.
Do be sure to think carefully before choosing LLU, whichever ISP you go with - I know several people whose speeds actually went DOWN after changing to it - a fixed-speed connection is always going to be a safer option.
If you live in an area which can handle it (I don't) I'd take a look at BEthere, also highly rated. It offers fantastic speeds of up to 20 mb or something incredible - though most get less than this, but still around 10MBs, way faster than other ISPs.) My friend, very techie, does a lot of torrents, changed to it and now has around 8mbs d/l and a big u/l speed too. He's very enthusiastic about it. I'd change to it if it were available in my aread.