You could buy a decent third party VDSL modem/router for under £60 and you will undoubtedly find it a superior product than any of the BT hubs.
Using a different router is not blocked by BT. Many people on this forum use one. Third party routers are easily set up. Most are just plug and play and if not it is only a case of setting the user name.
EDIT: The Ombudsman won't do anything until you have gone through the BT complaints procedure and assuming it has not resolved your problem you must then get a deadlock letter. Once that has all been done the Ombudsman may then become involved.
I didn't say you should buy one only that you could buy one in response to your comment "I would get another router, but BT have made it so difficult for this to happen, as they lock a lot of features to prevent this"
If your HH5 is faulty BT will only replace it with the same model. You should have a read through this forum about problems with the wireless amongst other things with the HH6 before you decide that you want one of them.
@KDowner I can assure you that BT do not 'lock a lot of features' to prevent use of a third party router, quite the reverse in fact. Many features of third party routers are not accessible to Home Hubs. I can honestly say that I have never used a BT provided router. As gg30340 has said, the HH6 is definitely not all it is cracked up to be.
There's a whole lot of people that would disagree with that statement and have reverted to the HH5. Shows you how bad they both are!
I never thought I'd defend the HH5 but if you look through the threads on here about it you will see many people have gone back to the HH5 because they have found it superior to the HH6.
Regardless of which is the better of a bad bunch, BT will not give you one for free and it is certainly not worth paying money for. If you really want one the best you can hope for is to try re-contracting and making it part of the deal.
As you make your living from the internet I would've thought the first thing you would've done was to buy your own modem/router.
All an ISP is required to supply is a wired connection to the internet the rest is just a sales gimmick. One ISP started it and the rest followed suit. No ISP's support WiFi.