Unfortunately, whilst the legal definition of a moped has not changed, so DavetG is technically correct, the way that two-wheeled motorised contraptions are built has changed, so Bonzo is also correct. As Iain's link proves, there are moped-built two wheelers that most certainly do have engines bigger than 50cc and, presumably, speed in excess of 28mph (it was lowered in Jan '13, Sen).

Wiki makes a distinction between mopeds, which is the legal definition, and scooters, which is the moped-build non-mopeds that Bonzo seems to be referring to. I presume that scooters basically require a bike licence. I would be very curious to know how many scooters are being ridden on moped licences. They'll be insured correctly, cos the insurance will damn well make sure they know what is what (there's money involved!), but if it looks like a moped... Who's checking it is & that the rider is correctly licenced? I don't know whether insurance companies are allowed to go to the DVLA to check licencing (and there's no guarantee the insurance is in the name of the rider anyway).