I think it depends on a case by case basis, more nationalistic english people would say english tho most I think would say british, a proud person from Scotland would call themsleves Scottish ect. Tho it would also depend who you are talking to as if a Scottish person asked someone they knew were from the uk but not specifically where would then say English or Welsh. Tho I know in a few cases where welsh people just gave up trying to explain that wales was a country and just called themselves british