We can only imagine which drivers are refusing to carry his assistance dog?

Yes - the nasty ones

So anyone who comes along and claims that their dog is an assistance dog.................and we have got to let them in

I can see the situation whereby someone develops a fictitious limp, and hey ho every man and his dog will be going home in a Taxi/P.h. It really needs clarifying - I am white - I take visually impaired people + dog............but I do not like animals in my cab out of choice.

People who use assistance dogs will have some form of paperwork or card to confirm that they are using an assistance dog.

How can a Recognised Assistance Dog be identified as different to a pet dog?

All disabled partners who have a Recognised Assistance Dog will carry a laminated ID card with a photo of dog and partner as well as the logos both of Assistance Dogs UK and the member organisation responsible for aftercare of the partnership. All Recognised Assistance Dogs wear jackets showing clear identification of the dog as a Recognised Assistance Dog, including the ADUK logo, or, in the case of guide dogs, will wear a clearly identifiable harness. In the event of the standard of the partnership falling below the necessary standard, all such identification is removed.

Where a clear allergy risk to a specific individual can be objectively identified by an establishment, steps should be taken to reduce this risk, but refusal of access for guide and assistance dogs based on the possibility that other people ‘may’ be allergic is unlikely to be classed as a reasonable or proportionate response.

A bit of a funny one here.

This could come up and I wonder as to whether ones spouse/children would be classified as "others".

We have a family car aside from my cab, so my wife does not travel in my cab very often. My wife is genuinely allergic to animal hair, so much so, it will cause her eyes and her lips to swell, also causing blotches to her skin. It leaves me wondering for those who are a one car/cab family as to whether they could claim exemption, as they do not really imo come under "Others", as i.e "Others" in the public.

As it's a licensed vehicle at all times, use for SDP is unlikely to wash. You have the option of running a private car.
Speaking of washing, is it not the driver's responsibility to clean the vehicle including any animal hair?

but refusal of access for guide and assistance dogs based on the possibility that other people ‘may’ be allergic is unlikely to be classed as a reasonable or proportionate response.

Right, not a problem as such. When there is no paper work/card...............the situation is what ? (excluding visually impaired as that is usually obvious).