Please ignore the RSPB distribution maps. In Essex (also not shown on the map) we have up to 10 wintering-even on the shore in east London. I have been to Norfolk in the winter and seen many before, mostly at Snettisham. The maps show the British race only, not the Scandinavian race which is found in the south-east. Your bird shows a dark eye stripe, which Meadow pipits do not usually have, so I think it is likely a Rock.
not meadow pipits as the one on the left has an unstreaked back and they both have dark lores and heavier bills than the 'pinprick' bill of a meadow. They're Rock Pipits, most likely Scandinavian Rock Pipits.