If I’m not mistaken they should do the work as long as your going from FTTC to FTTC, if your full fibre FTTP then I don’t think so.
For a peace of mind give the team a call.
NOW Broadband Members can call us 8am–8pm, 7 days a week.
In theory it should just switch you7 should get a message from the old provider along the lines of "sorry you are leaving us , here are some offers to make you stay ..."
As you have a voice line only , with no DSL on then it may require an engineer to visit to set things up , what package form now have you signed up to?