In message . com,
AndyColeman writes

One concern is the escalators. I have seen signs on some escalators
indicating that dogs need to be carried. As she is 30kg this could be
difficult on a long escalator. I can pick her up when get on and off
but it should be safe to put her down while traveling up.

There is no regulation to prevent you taking a dog on the tube through
the central area. However, if you cannot carry the dog on the escalator
then you are supposed to ask a member of staff to stop the escalator so
you can walk down/up. This will only normally be done at quiet times
outside the rush hour - since Waterloo doesn't have quiet times, you'd
probably do better to take Paul C's rather roundabout route.

--
Paul Terry