The NHS may be able to provide a wheelchair free of charge, but does not supply scooters. The NHS will assess the person you look after so that they can choose the right one (there are different types available). The assessment is done at a wheelchair assessment centre or clinic.
And check this out...
Using a mobility scooter or powered wheelchair
You have to follow the rules of the Highway Code, whether you are using the footpath or the highway. Following some safety tips and keeping your scooter in good condition are also important points....
From the article: He told Police Review that the problem of dangerous riders is becoming more prevalent because of an ageing population and the ease with which scooters can be bought. He said: 'People can just buy a mobility scooter, sometimes off the internet or somewhere else, and literally just get on it.
Apparently they are quite easily and inexpensively available in the UK from a variety of vendors. Although the NHS doesn't fund them at the moment, some private insurers may. However, they are not terribly expensive and most people of some means who need one seem to be able to get one