Home Move is not an issue, just done it myself a few weeks ago and BT have migrated over my services for free provided I entered another 12 month contact (which I did).
I would just get the package upgraded for peace of mind and enter a new contract.
If they are outside of their contract they could switch providers as well.
Thanks for the reassurance re Home Move and BT.
To be honest I think (like many others) they've paid over the odds over the years for the telecoms services, and my thinking was that I was going to encourage them to take up one of the new customer offers (from BT or someone else) when they move into the new place, to try and tip the balance back in their favour. However that will obviously have to wait!
They are out of contract for their broadband, but have paid Line Rental Saver with many months still to run so are kinda tied to BT. I did look yesterday at how long it would take to migrate the broadband only over to Plusnet, and going through the order process the earliest date offered was 1 December... by which time they will have racked up yet more excess charges for going over their monthly GB allowance this November!
So I think it's a case of them staying with BT and bumping it up to an unlimited package... I will see what can be done today, hopefully they'll be able to quash the excess charges as part of the upgrade sales process.