I don't have a Openreach modem but I don't like to have many things plugged in as I have 4 wired devices and if I use the modem which will use up a port on the router then I will have to use a switch.Doubtful for £80.
The Openreach modem is very good, why do you want to change? Is it aesthetics?
If you restart a router with built in modem, DLM may kick in and apply interleaving and/or reduce speed.
I'm on BT Infinity 2 using the HH5 with 65Mbps down and 20Mbps up but want to use a different router than the one BT has supplied which I can sell to use the money to buy a new router, my budget is £80.
Billion 8800NL is well within your budget. Rock solid sync on my dodgy vdsl line.
Only 2.4Ghz and 1 gigabit port, 3 10/100 ports but thats the downside of the smaller budget.
I'd recommend it for its stability.
I think there's a TP Link TD-W9980 you could look at, it doesn't support MER for Sky Fibre at this time, but shouldn't be an issue for you.