In the autumn of 1981, when running as a popular sport was in its heyday, Geoffrey Cannon was writing a column firstly in The Sunday Times, and later in "Running" magazine. He gathered a group of new runners who were intending to run in the 2nd London Marathon in 1982, and wrote about their training in the magazine. Most of this group lived around London, and a number of training groups were formed. One was in South West London, and met at the White Hart pub, at Kingston Bridge, on Thursday evenings for a training run followed, as you may guess, by a drink in the pub. You can read more about it in this link about the origins of the Serpentine Running Club.
Chris Brasher had recently opened the first Sweat Shop in Teddington and, hearing of this group, offered to provide some T-shirts for them. It turned out that he had already had the shirts printed, with the well-known foot on the back, and with the name, "Sweat Shop Striders".
The runners thought that "Striders" sounded a bit too keen, and one of them suggested that the "Sweat Shop Stragglers" would be nearer the mark - and the name stuck. The original "Striders" T-shirts naturally became collectors' items, and some may still survive.
For the record, the original group that became The Stragglers were:
Bill Brown, Will Chapman, Lucy Deane, Keith Haworth, Peter Lordan and Chris Turnbull.