It seems even bus companies are confused as to whether it is law or just good manners. After a bit of googling:
"Arriva
When not required by a wheelchair or scooter customer, the wheelchair space on accessible buses can be used by up to two buggies, prams or pushchairs. Use of the wheelchair space by any customer is subject at all times to enough space being available and the discretion of the driver.
During travel, buggies, prams, pushchairs, wheelchairs and scooters must be securely positioned so that they are stable and do not cause an obstruction or hazard to other customers. Drivers will advise of any circumstances where it is not possible to allow customers to travel safely; this includes their own health, that of the customer, other passengers, members of the public, or the security of the vehicle and its equipment.
The driver can require that pushchairs and all types of buggies are folded at busy times, or to request occupants of the designated area to move elsewhere on the vehicle if a customer wishes to board with a wheelchair or scooter. You should co-operate in allowing proper use of this space by vacating it if necessary in favour of a wheelchair or scooter user.
Stagecoach
Subject to space being available and the discretion of the driver, we will carry small prams and unfolded buggies on low floor buses within the designated area but only when it is not required by a passenger in a wheelchair or approved mobility scooter who has absolute priority by law. Prams and buggies must not block the aisle of the vehicle at any time.
You are, however, required by law to ensure that the designated wheelchair space is made available if a customer wishes to board with a wheelchair, a disabled buggy or approved mobility scooter.
You are required to co-operate in allowing proper use of the designated wheelchair space by vacating this space if it is required by a customer in a wheelchair, a disabled buggy or approved mobility scooter including repositioning small prams, folding any buggies and storing them in the luggage space. Failure to comply with this requirement will comprise a breach of Section 3 above and may lead to further action as set out in that Section.
EYMS
Can I take a pushchair or pram on board the bus?
When not occupied by wheelchairs, the space provided may be used for a pushchair. At busy times you may be asked to fold the pushchair. Priority should always be given to wheelchairs. For safety reasons pushchairs, shopping trolleys etc. must never block or partly block any gangway. Only pushchairs and baby buggies which can be folded are permitted on our buses. Non-folding pushchairs and prams cannot be carried.
First Group
Wheelchair users have priority use of the wheelchair space. If this is occupied with a buggy, standing passengers or otherwise full, and there is space elsewhere on the vehicle, the driver will ask that it is made free for a wheelchair user. Please note that the driver has no power to compel passengers to move in this way and is reliant upon the goodwill of the passengers concerned.
Unfortunately, if a fellow passenger refuses to move you will need to wait for the next bus."
But they do all make it clear that a wheelchair has priority in a wheelchair space.
(I chose these bus companies as they are ones I've heard of or used).