Do you have a maximum budget? Do you know what sort of options you have available (ie FTTC,FTTP, ADSL, etc)? Check on the BT checker
to see what options you have available and it will also tell you the range of potential speeds to your number. Do you have Virgin media available?
Depending on the answer then there are many potential ISPs such as BT, PlusNet, Zen, Uno, Virgin, AAISP, Sky, etc, etc. You can do some comparisons to narrow it down a bit on Thinkbroadbands homepage via this
There are some ISPs that are having issues but this can ebb and flow. The one that seems to be the biggest problem at the moment is SSE with reported congestion at peak times. Talktalk have had their problems in the past although things seem to have gone quiet on issues with them recently.