Hi Maggie
Based upon your statement that in the 1911 census he was unmarried I have just run a search on Free BMD and got several hits but not from within your specified area.
If you search on Frederick Pickring and a Mary 1911 onwards and all counties = no results, put the e back in and there are 15 between 1911 and 1952.
Run the search again using his name and also Mary Ann or Mary Anne = no results.
It is as you will know I am sure, quite possible he married away from his hometown, so if you replicate what I did then perhaps one of those 15 may be yours?
I so hope this helps in a small way
NDRFT