One way to find dairies, is to see the list that were granted milk licences in the council minutes, such as this one from 1934.
From the minutes of the Public Health Committee
4th December 1934
12. Milk Licences
Applications to use the designation “Certified,” “Grade A (tuberculin tested),” “Grade A,” or “Pasteurised” milk were submitted, and it was Resolved, That licences be issued as follows:-
Express Dairy Co. Ltd. : 229 Western Road
W. and J. Hill Ltd. : 257 Northborough Road
Hugh LaBroy : 84 Seeley Road
D. J. Price : Devonshire Dairy
H. E. Robinson : 356 London Road
Royal Arsenal Co-operative Society : High Street Colliers Wood
United Dairies (London) : 251 London Road and 198 Streatham Road
Source: Minutes of Proceedings of the Council and committees, Mitcham Borough Council, Volume 1 1934-35, pages 63-4
Minutes of meetings held by the Mitcham Borough Council are available on request from the Merton Heritage and Local Studies Centre at Morden Library.