You are from the UK so get a bike capable of coping with typical UK winter conditions.
Your 2x11 miles is starting to become a Long Commute where efficiency becomes important.
I suggest a road bike of the "winter training" style (eg Kinesis TK), a light touring (Audax) or a cyclo-cross with disc brakes (Boardman make a nice one).
Make sure the bike has clearance for 28mm tyres + full-length bolt-on mudguards. I would suggest standard 32 spoke wheels, nothing special or fancy.
You will probably want a rear luggage rack with a single pannier.
In winter you will need a good lighting system and possibly a backup lighting system.
Fit some puncture protected tyres.

You will need a Plan B for the few weeks of freezeup. This may be some studded winter tyres (you need cyclo-cross style clearance) or public transport or a car.

Figure out the annual cost of not using a bike to get to work. Multiply by 5. That is the amount you can save, so don't skimp on the initial spend.
Make sure you have 3rd party insurance. Check out if you can buy tax free through work.