We have a blue badge so will take that. Having said that, when we recently went to the London Aquarium, where carer also goes in free, they did not even ask to see the badge (although they could quite easily see a wriggly and quite loud small person trying continually to escape from my grasp as I explained that we could not stand in the queue etc!).
One of our tutors recently took DS to the London Zoo just for an hour just to familiarise him with the environment (he is always better the second time around in any new place!), it worked quite well and they were let in free.