The only Alfred I found in Staffordshire in 1841 is exactly the right age, 20, appears to be a Male Servant for a grocer, living Bird Street, St Mary, Staffordshire. unfortunately it would appear that he claims not to have been born in County.
In 1851 I was wondering more whether Alfred was working for Richard Simpole at the time he was married, he seems to be a fair bit older than Alfred, being between 45 - 49, living in Tongate Street, St Mary, Staffordshire so the right area for the Alfred above, occupation Checker, of what isn't clear. And a probable Mary Ann Perry living Friar Street, St Mary, Stafford, father and some of the family were shoemakers and shoebinders, but who may just have been a friend of Hannah.
In case you don't have the Austins in 1841 here they are
Red Lion Street, St Mary and St Chad, Stafford
Thomas Austin ShoeM J Y
Elizabeth 50 N
Caroline 15 Y
Hannah 15 Y
HO107/1010/2 Stafford Folio 32 Page 19
I can only make a couple of suggestions, that you check the films for the Churches in Lichfield for a baptism of Alfred, it could have been at the Cathedral, St Mary, St Chad or St Michael. There were also a couple of Methodist Churches but the dates don't always seem to be applicable. If you aren't able to get to the Record Office, you may be able to order the films through your local LDS Centre, I know searching each individual church might be a long winded way of doing it but there doesn't seem to be many entries transcribed on the IGI and that might be the only way of doing it.
If you are able to get to the Record Office it would be worth asking to see whatever documentation they hold for the schools in the area at that time, Thomas may well be mentioned.
Mary
Added after - I know there's not a lot to go on except the possible area of St Mary's but I thought it worth looking through the 1841 census to see if I could find a school teacher and have found a Sarah Clarkson 55 Schoolmistress born in County, living on Donn[Dam] Street, maybe lodging with a Hannah Dunstone and her family, and a female servant, Frances Toft and an Ann Toft. There's also a Mary Harris, 50 Schoolmistress, not born in County, living Sessions? Lane with Thomas Harris 23 a visiting clerk and female servant Hannah Gee.
Of course this is nothing conclusive but would make me wonder whether they were predecessors of Thomas or if he had been working there and already died.
Have you joined the local Family History Society for the area? there are often books, sometimes in the form of diaries which local societies may hold giving details of events in the area, births, deaths etc. if there was such a thing I'm sure a local schoolmaster would warrant a mention.