No it doesn't. It applies to wheelchairs.
If someone can't fold they could ask for help or get off and wait for the next bus.
The needs of a wheelchair user do not automatically take priority over those of another disabled person. If you check the equality act legislation you will see that it applies to anyone with a disability.
The bus company have a legal obligation to make reasonable adjustments for a parent who cannot fold the buggy due to severe arthritis and the fact that there is no dedicated space for them does not change this.
Making someone get off a bus because they have arthritis is just as discriminatory as refusing to allow a wheelchair user on not to mention the problems that waiting for another bus in the cold and wet could cause to someone with arthritis.
It's easy to say "ask for help" but what if there is nobody around to help unfold the buggy at the end of the journey? It would be ideal if the driver were to help but what if " elf n safety" stops them.