Typically 1-2 weeks. Your provider will send you a new router, let your old provider know, and get everything set up ready to go live as soon as possible. Normally setup is as simple as plugging the new router into your phone line, but if there are issues you may need a appointment with an engineer which can take a bit longer.
If you don’t have an existing landline, or you’re moving to Virgin Media or one of the new FTTP providers, they will need to run a new cable from the street to your property.