It depends on how "instant" you want. I am on NTL Broadband at 600 and I don't have a problem. My download speeds are around 70kbs except for yesterday when it dropped to around 35kbs but still better than 3.5 on dialup.
I use BTYahoo Broadband. Costs £29.99/month. I really can't complain even though, like most people, we like to have a go at BT from time to time! It's always available, fast and is being improved. Witness the recent update to their webmail. NO, I don't work for BT or own any of their shares!!
i think you have a problem,i am on ntl 600 and i get 70kbs or more sometimes.it does sometimes drop below 70,but not for long .i used to get about 17 on 150k.i know you hear a lot of bad press about ntl,but overall i am happy to pay my £24.99 a month.you could do a lot worse.peter.