My poached eggs were ruined

I am so excited! Whilst poaching two eggs for my lunch I caught sight of a brand new bird in my garden. I was looping the loop so much I forgot about the eggs, but did manage to grab the camera. I couldn't believe my eyes. I am so not confident with my ID's of non-garden birds. It was walking, not hopping, and eating seed from a snow covered gravel area. My garden isn't very big, there is no grass and no pond.

Is it a pied wagtail?

Pictures taken through patio doors

It stayed for what seemed like ages, and wasn't worried about seeing me, until my dog appeared next to me, then it went.