Yes, it's not a problem.Do they except bikes in all there hotels.
Yes, it's not a problem.
Yes, it's not a problem.
There are a few Travelodge that don't but I forget where and I think it's mentioned in descriptions online.
"Hub by Premier Inn" don't, but that's stated in their policy, I think, plus it'd be bordering on physically impossible in those small cleverly-styled rooms.
Yes they're city centre hotels and you'd struggle to get a folded Brompton in there !