Trying to ID tiny bird


tiny little bird bird in our garden today which is wooded.It was about the size of a wren and had very white fluffy breast,it's back was brown. It was almost mouse like in it's movements in and out of climates on the wall. Can anyone help with identification ? Lochwinnoch Scotland.   We have moved here from Argyll and there are quite a few birds in the garden that we have never seen before such as nuthatches.