I know my ancestor was born in Sutton Coldfield in 1846/47, and I have found what looks like his birth record in 1847 Q4, but the district is given as Lichfield. Was Sutton Coldfield in Lichfield district in 1847?
I have just noticed your question. A lot of my relatives come from 'Sutton Coldfield' They lived on the borders of Staffordshire (Dist.Lichfield) and Warwickshire( Dist.Aston) at Watford Gap/Four Oaks. People of this area tended to class themselves as Sutton folk, but it may have been nearer and easier to go to Lichfield to register births and deaths rather than Aston.