Whether a mobility scooter is allowed in a particular building can be dependant on a number of factors, appropriate access being one of them, not only access to enter the building but once inside if the building has several floors then ideally you are going to need a way of reaching those floors, quite expected would be for a lift to be in place within the building.
It is common place for supermarkets to cater quite well for mobility scooters and also wheelchairs, indoor shopping centres and stores that allow for a person with mobility needs to move between display units easily.
In many cases it wont so much be a matter of whether a mobility scooter is allowed into a particular building but whether the building can appropriately allow a mobility scooter user to move freely throughout the building and without any unnecessary risks.
Accessibility is something that more and more businesses try to cater for as much as they possibly can, also local councils take this into account when planning development and regeneration within local areas.
With modern buildings there is plenty of thought put into making a building accessible to those with mobility needs way before any actual development begins, whereas with older buildings (depending on the age of the building) they might not be so mobility friendly, and by mobility friendly i mean the original building design and layout, not the people who work within the building.
Where possible though, even in quite old buildings, adaptations are made to make a building more accessible.
So if you find yourself wondering if mobility scooters are allowed in a building it will depend on the particular building that you want to access, whether they have what is needed in place for your safe entry, exit and manoeuvres around the building or whether there might be a special type of flooring in place inside the building or parts of it that could become too easily damaged from a mobility scooter being used on it.