The ground will need work. Also why do you assume no extra topsoil needed? A quality turf costs £3/m2. That job above at 60m2 / £240 is a joke…and from looking at it I guess you get what you pay for.
I’d be at least £750. But then I’d probably not be fussed about getting the job as I’m so busy! But a proper lawn lay needs proper prep work if you want a good, level, healthy green lawn that lasts properly.
OP’s 7×8 £123 +VAT from a local supplier for their premier stuff, £95 +VAT for hard wearing. Having seen their fields it looks like good stuff.
But yeah, proper prep is the key, I reckon I’m gonna have to excavate a load of clay from mine or dig in soakaways , not decided yet. Gonna be a bawache either way