Should I change my Internet Broadband provider?
Today, Broadband Internet providers are a service provider very much like Insurance, Electricity, Gas, etc.. They all have a contract of about 18-24 months long, that comes to an end, and after that time you can switch, without any penalties, to another provider.
The answer to this question is almost always YES, if you are not happy with your service or want to save money.
When is the best time to change my Internet Broadband provider?
The best time is after your contract ends.
Be careful that your contract is not renewed as a way to keep you hooked in for another 18 months. E.g. Accepting a new "upgraded" router will usually come with a contract renewal. Also, a performance boost to match the competition (Looking at you VirginMedia here) will come with a contact renewal.