MOT doesnt require a spare and there is no legal requirement to carry one. The only thing is that if you do keep a spare, it must have legal tread otherwise you will fail the test. A lot easier just not to have one in the first place!
AA have got me home with a puncture before when I had no spare. They might make a big fuss but at the end of the day if your car is legal on the road, taxed/insured and roadworthy they have no right to refuse to help if you are paying for their service. In a lot of cases people with big rims might be running spares wheels that are completely useless as theyre so undersize that it would be dangerous to fit them and drive on them.
So Ive always run without one. Carrying a spare is crazy if you think about it- OK If I got a flat I could crawl around under the car in a muddy puddle getting my legs almost run over by every passing lorry, in the pissing rain and pitch darkness, trying to fiddle about releasing the cage and getting the wheel out, then going to all the trouble of knocking the bolts off with a wheelbrace that hardly works, and a jack that will either damage my sills or collapse and snap halfway up. Or I could just ring the AA/RAC. Im perfectly capable of changing a wheel, but would I want to if given the choice? No.