It sounds like you are taking the right option.
You do need to check what contract you are on before switching. Some contracts last for 12, 18 or 24 months after which time they go onto 30 day notice contracts. If it is likely to be a bit sticky getting out of the contract, it would be worth detailing your problems in writing to the ISP and giving them a "last chance" to fix things before stopping payments. If they then tried to enforce a contract, you would be in a strong position particularly if, as is likely, you can prove that the letters arrived (recorded delivery) but you got no response.