I moved from pipex earlier this year over to bethere.co.uk.
I now get 16Mb/s download and 1.3Mb/s upload for the same price, however pipex have tried to collect the money and have had to refund it twice telling me the account was definatly closed and no more money would be taken, still they took it and had to refund it, so i cancelled the direct debit at my end and they then called me and told me i owe them for three months worth of internet.
I had minimal problems with Pipex, except for once when they closed off my account on a sunday lunchtime for owing them 84p. and the office was not open till monday morning to pay the charge. when they then tried to take the money, they said they couldn't as it was less than a pound so they would just charge me more next month and put my internet service back on. so i was without internet for a day for no reason at all.
I would still recommend pipex if you wanted to go with them, but i'd also tell you to cancel the direct debit at your end when you close your account as well.
M.