I have a big problem in that I weigh 120kg (approx 19 stone).
I doubt that's really a problem. I weighed more than that when I started e-biking on a standard "nothing special" 700c wheeled hybrid ebike. You just need to be aware you are over the usual 100kg most makers recommend, and take care not to over-stress the motor or bike in general, use the gears properly to keep your cadence up and not just "ghost pedal" so the motor is forced to do all the work. Both my hybrid bikes (both £1000ish lower-end crank drive) would and still do climb a 15% hill.
The only issues I really had was tyres; most 700c road tyres on hybrid/commuter bikes are only rated to about 100kg... I blew out the side-walls on two (over 1500 miles) for no obvious reason!
Yes, Woosh's Big-Bear is a pragmatic solution, but I'd also look at some of the £2k Cube hybrids given your fairly generous budget, and put some puncture-proof Marathon Plus tyres on it for road commuting.