In short, yes.
Long answer.
The first place that bike manufacturers cut corners is the wheels, the average bike buying public recognise names like FSA (for finishing kit), 105/Ultegra/Veloce etc (for groupset) but most have no idea about wheels. You are right, on the average £1200 bike the wheels will be cheap ones, certainly, rarely, with a retail value of over £100.
Changing them will make a big difference, I have found. The first time I did just this I swapped a pair of cheap Vuelta wheels for bottom of the range Shimano jobs which transformed the bike from something I hated to a joy to ride.
My current favourite road wheels are Shimano 6700, light, fast spinning and bombproof. Can be bought for ~£200 from the likes of Merlin etc.
No doubt someone will be along in a minute expunding the virtues of Mavic wheels (you know, the ones with the completely unpronounceable names), I never have got on with them, YMMV.