In this case, stopping the payments should do it, but....
The contract which every ISP has with the owner of the phone line (which is normally BT) contains a protection clause which enables the ISP to block BT from allowing another ISP to be on the same physical line.
So if you have eg. a 12 month contract and want to back out after 9 months, you will not be able to get another ISP on that line until you have paid for another 3 months, or settled out with the original ISP by paying a 3 month block. ISPs tend to be quite aggressive on this because they don't want somebody to stop paying and then get service from another ISP.
I had some hassle with Clara once who cut me off for alleged copyright infringement (they refused to provide me with evidence, citing the data protection act
) and they blocked the line until I paid them off for the balance of the year. Clara confirmed they would cut you off purely upon receipt of an automated email complaint....
I got around it by getting BT to renumber the line. It was an analog line purely for ADSL so its number was not anything important. Renumbering cuts off the ISP and you can then (usually) get another ISP to provide a service. In fact it was BT who suggested this
They said the only other time they can get an ISP to vacate a line (against the ISP's wishes) is if the ISP has gone bust.
A neater way is to have two analog lines (probably quite a common thing, now that BT have dropped Home Highway) and you can get a new ADSL service on the other one, regardless of a dispute with an ISP on the first one.
In a business context, I would recommend every business (using ADSL) to have at least
two analog lines. Yesterday, we got hit by a spammer who sent us about 20k emails, resulting in loads of bounced emails being transmitted by our email server, and we got all our outgoing ports disconnected by the ISP - without any warning. It took a day to sort it out. A lesson learnt. I don't think ZEN would have done this but I am already with ZEN at home and that's where our backup server is, and one can't have the same ISP for both locations...