In view of the similarity of names, I'd assumed that Clayton Bros. were connected in some way with Clayton Mayers, but having looked I'm unable to find any written evidence to support this in either Glen's or the Stewart's notes (but see below).
I was under the impression that C.M. were not at any time south of the River Thames (in the London area), but the relief wording on the base of this carafe/water jug includes the London postal district of S.W.18, which covers parts of Wimbledon and Wandsorth - which are certainly south of the river.
The full wording is.........CLAYTON BROS. LONDON S.W.18 - RD. NO. 785302.... and this number is confirmed by the 'Blue Book' as being registered on 28th July 1933. Height of this piece is c. 6.5" (165mm).
Being very inefficient, and working back to front, and having typed the above, I then entered Clayton Bros. on the Board's search and came up with..............http://www.glassmessages.com/index.php/topic,25679.msg202682.html#msg202682
........... a thread which started in 2009, and appears to have run for a couple of years.
I have extracted from this thread part of post No. 6 from David W dated 04.11.10, in which he comments..........
""Thanks to all who are keeping an eye out for 19th or 20th century London glasshouses. The latest issue of Glass Circle News has just come up with a mould-blown (or press-moulded) bottle-jug with applied handle and moulded in the base Clayton Bros. London, SW18. Rd No. 735702 (i.e. 1928). It apparently belongs to a descendant of the Clayton family but he does not know anything about the firm. This is also a new one to me. Can anyone provide further information on this firm"".
Obviously, I'd forgotten this matter completely.............so, does anyone know if any further information was found for Clayton Bros., or did the matter die the death? Certainly nothing further was added to that particular thread.
Would seem that David didn't add any images for 735702, although judging by his description of the piece it may well have been similar to my Rd. No. 785302 - perhaps carafes/water jugs were very common utility items in the 1920 - 30 period.
As Glen has pointed out previously, C.M. were agents, wholesalers and distributors only, and not manufacturers - so are they one and the same, or were there two companies by some remote chance? Does seem a big coincidence if they were two separate companies.