Hi, Jazzy!
I'm sorry but I'm afraid I cannot really help you here as I don't know much about it.
I know some of the names you mentioned, Becker, Barratt and Knight especially. I think they all became known around the mid 1950s.
The West Hants Club (Bournemouth )is of course very famous, as you 'll know.
It hosted the British Hard Court Championships there
for many years - I think the first one was late 1930s?
Are you looking for Davis Cup matches in which these players performed? or could they have been playing in the British Hard Court Championships?
I'm wondering this as they were staying so nearby?
I've tried googling this but can only come up with names like Virginia Wade, Rod Laver, Ken Rosewall and Ann Haydon-Jones as having played in the British Hard Court Championships.
Sorry, Jazzy ! not much help!