Diocesan House, Verulam Road, St Albans, 1940's
I have ready access to a 1949 St Albans Street Directory and I can tell you where it was. If you enter St Albans along the road from Redbourn (the old A5) bear right at the Total Petrol Station. On your left you will pass Victoria Park, then a large buildong which used to be the St Albans and Mid-Herts Hospital. Then there is a side road (Church Crescent) and about half a dozen houses. Next comes Christ Church (I think now) offices and beyond that, in 1949 there were three houses before you get to the turnings of Britton Avenue and Gombards Alley. The middle of these was Diocesan House. (There was an argument in the press a coupe of years or so ago about the yew trees which were threatening to push a wall over into the footpath - and this may have been Diocesan House or one of its neighbours.)
The entry reads "Diocesan House (Sister Superior, warden)" and it seems very probable that it was run by Church of England Nuns and provided facilities for unmarried mothers. Maybe if you wrote a letter to the Diocesan Office, St Albans Diocese, Holywell Lodge, Holywell Hill, St Albans, they might be able to say more about the home.
If you can add to the information given above tell me.