This is a big subject. These were huge firms selling all kinds of seeds, for agriculture, for gardening and from the start of the last century for Golf. Ironically the types of grass seed they were originally interested in were to produce thick lush grass for cattle to graze and grow fat on. Not ideal for golf. By 1852 Suttons had 54 separate mixtures on Sale.
Apparently it started with Carters at Walton Heath. Suttons were the bigger firm but slow to realise how big Golf was becoming.
Apparently the basic modus operandi of the earlier seed merchants (perhaps in the first decade of the 20th century) was to just throw anything and everything into those grass seed bags under the theory that something should probably grow! Unfortunately, that approach created something of a "grow-in" mess on a few early courses apparently including NGLA.
This was a real problem on all the seeds the firms were selling. Suttons sold on purity of stock, meaning you needed to use less, and Carters on how quickly they could establish a playing surface. The adulteration (bulking up) of all types of seed was so common that various Acts of Parliament tried to regulate quality. Old, dead and even similar looking seeds would be added.
Both firms were active in the wholesale slaughter of Worms!
Influence is hard to know. However they were powerful firms and each offered practical support if you bought their seeds. Both firms targeted Greenkeepers. Carters produced an annual hardback, “The Practical Greenkeeper” which had an essay from Simpson in the English edition and Tillinghurst in the American one. Suttons responded with an essay competition for Greenkeepers and later their own pamphlets.
Carter’s used to employ the contractors and add 10% offering the client a one stop solution, and the list of Architects in their camp was most impressive. Braid, Fowler, Simpson (who appears to have crossed the floor in the late 20’s) and (dare I assume) Tillinghurst. The also used Peter Lees in their advertising.
Suttons entered the field properly with Colt in 1909.
There’s a lot to find out.