+1 for two bikes for you, if there is one sure fire way to ruin a bike it’s using it for commuting.
Unless you are very diligent with cleaning and maintenance or only commute in good weather then you will go through more drivetrains, cables and tyres than your wallet can handle.
Even with a short commute like that weather and use will take it’s toll and you’ll soon get bored of cleaning all the road grime off…
Buy a decent hardtail for £1200 – £1500 and then use the rest on a decent but budget roadbike/hybrid for the commute.
If you absolutely must only have the one bike then at least get a 2nd set of wheels with roadie tyres, no point wearing the knobbles off your decent tyres.