In 1974 , under the Local Government Act 1972 , the county was abolished and its former area was combined with Cumberland and parts of Lancashire and Yorkshire to form the new county of Cumbria . In 1974 , under the Local Government Act 1972 , the county council was abolished and its former area was combined with Cumberland and parts of Lancashire and Yorkshire to form the new county of Cumbria , administered by a new Cumbria County Council .