Yellow wagtail (?) near Euston

I have difficulty telling the yellow wagtail and the grey wagtail apart. I thought I had it clear with one book , but now not so sure.

The yellow wagtail is found near slow-moving water - lakes and marshy pastures so I wonder if that was what I saw looking out the window this afternoon while photocopying. There was a bird with a very long bobbing tail with its back to me as it preened. I wondered if it was a parakeet with wagtail-like movements, but when it finally finished preening I saw it was either the grey or yellow wagtail.

I think it is the yellow wagtail as the nearest water (besides the fountain in the courtyard) would be the regents canal which is slow moving water. But my Collins Bird Guide says: "compared with other wagtails, Grey Wagtails has longest tail....Constantly pumps its long tail, and so strongly that whole rear end rocks with it". That describes the bird I was seeing. So perhaps "at times also on lakeshores and slower rivers" is the clue here.

If I can't tell the difference from locaton, I am going to have problems - they don't get near enough and stay still for me to check them out properly, even if I did have my bird book handy.