Accept the fact that every single ISP provided freebie router is shite (in all respects, not just wifi) and you'll get less hung up over which ISP is better.
All the freebie routers are ones the ISP can bulk buy for sub £20, which gives some level of understanding how much research and development has gone in, and why all the firmwares are appallingly bad.
I did read a couple of years ago that ISP`s made it difficult to use 3rd party routers, I don`t know how much truth there is in that but I believe it was to do with some settings that the ISP needed to give but weren`t playing ball.
I never looked into it because my VM router is fine at the mo, I can get wifi in any part of the house and even on the road in front (which is handy for using my laptop on the missus Panda).
Nope. None of them do. My primary ISP, Zen Internet, actively encourages it, and provide reasonable support when things don't work. My secondary ISP, BT Business, give me all the details to get a 3rd party router working.
The HH4/5 is probably one of the best "free" routers, but is still utterly, utterly shite. Its reasonably stable, reasonably decent wifi, reasonably decent modem. But spend good money on a router, you will see how shite *ALL* ISP routers are. BT, Sky, VM, Whorehouse. They all provide the cheapest crap they can get away with - the UK ISP market is incredibly competitive, which is why we have some of the fastest speeds at the lowest costs.
And I say that knowing my brother's 2 premium broadband routers had desperate issues doing their core function (routing), which still hasn't been resolved, but support and I came up with a viable, robust workaround.