Hi Paul, and
I don't use Fibre myself, and am not greatly technically minded when it comes to this stuff, but I too did have similar problems with more than one router, on my ADSL2+ service. It sounds a similar problem to your own, in so far as I understand it, as I had a network connection, but the Internet (PPP) kept dropping, sometimes for a few minutes, and sometimes for much longer. Rebooting the router(s) (Billion 7800DXL and Billion 7800N) seemed to solve the issue for a time, but it often reoccurred at random intervals. IDNet could not find any problems on my line, but suggested setting the router to PPPoE rather than the default PPPoA, which kind of resolved the issue, in that the connection was then more stable, but it was also slower.
After putting up with this for ages, I finally decided to try a different brand of router, and bought a nearly new Asus DSL-N66U off of eBay, which has worked more or less faultlessly since it was installed. This is a modem router, but I do know that Asus also make non-modem routers, such as the RT-AC86U, which, if you check out reviews on Google, seems to be highly rated. Unfortunately, it doesn't fall within your £100 budget, but you may be able to pick one up off eBay cheaper than purchasing new, should you decide to go down that route.
I'm not personally recommending that you buy that router, or indeed, any other router, but just thought it might be useful to relate my own experiences, as there seemed to be some similarities with your own.
Hopefully someone with some better technical advice will be along in due course.