Unless you can change the login details on the Talk Talk router, its not going to work.
Many ISP provided routers are locked to their service, to keep things simple.
You could probably buy something locally from Argos or PC World, that should work, but I doubt you could get BT to reimburse you. It would either have to returned, or kept as a spare.
Many shops seem to be concentrating on 4G routers, as normally ISPs supply their own.
Cheapest would be TP-LINK Archer VR400 V3 £57.99 from PC World.
You would have to configure it yourself, but TP Link stuff is very easy.
No good if its not available locally.
You can get a Smart Hub 2 for under £35 on Amazon and a spare’s always useful even when BT get round to sending you one.
Don’t be put off if it says it’s the FTTP version. It will work with FTTC/VDSL as well and the old cable from your Talk Talk should work.
As a self-confessed non-techie, probably best to stick with a BT product. Even an ancient Home Hub 5 would do you in the short-term & shouldn't cost more that a fiver. As @WSH said, some form of backup is always useful in any case.
You're looking at it from the wrong perspective. This is BT doing a sterling job of setting your expectation levels early! 😁