hello op, :) I have been a guide dog owner for the past eighteen years (on my third dog now).
under the equality act it is an offence to put a disabled person at a particular disadvantage over their able-bodied peers, therefore disallowing the dog into the dentist is potentially up for question.
That being said, if the dentist are adament that the dog is not allowed within the actual surgery they would need to make this clear under their equality policies in order that owners be aware beforehand. If not then they would be obliged to look after the dog while you enter the surgery, although it is up to you if you would be happy for that to happen.
The law on public establishments e.g. shops/restaurants etc is very clear. But with more private ones it is less so, and is IMO much more about personal preference than genuine health and safety/hygiene.
There are two exceptions to this afaik:
The first is in kitchens where food is being prepared, because "no animals" is a part of the health and hygiene laws. This applies only to the actual kitchen area of a restaurant though and not the seating area, so a restaurant where food is prepared in sight of the customers still wouldn't have the right to disallow a guide dog.
The other is places where there are other animals present, and where the presence of a dog could be seen as detrimental to the wellbeing of the animals. Examples of this are London and Bristol zoos which don't allow guide dogs at all, although afaik they have kennelling areas should you wish to bring your dog, and they will look after them for you. Not all zoos have this policy, but many which have areas where animals roam free do because it is much easier to say no dogs than to be sure that a guide dog wouldn't be taken into an area where e.g. monkeys were running free. Paignton zoo however do allow guide dogs, but they ask you to keep them away from the big cats as this distresses the cats. Having been round a zoo with a guide dog though it's not something I would recommend. 
Wrt dentists/hospitals/clinics, I know of at least two large hospitals in the UK where guide dogs have been allowed on to the ICU, so I am not convinced of the argument that there are valid reasons not to permit them other than personal preference/ignorance on behalf of individuals.
It's a difficult one to challenge though especially if you are a first time guide dog owner. But it might be worth having a word with your guide dog engagement officer so they can perhaps go and have a chat with the dentists. Which branch are you under?