Thanks ever so much - it was the clipping you attached from 1893 that was actually what sparked off my hunt. Having begun my search at the library through the Blyth News, I have found a few match reports - the Rovers not being very successful at all it appears, losing every game and not scoring any points!
Sadly for the Rovers, the last mention I can find in the Blyth News was from 6th Jan 1894 with a match report from a game against Choppington - I could find no mention of rugby in Blyth again until a match report about "the newly formed Blyth Rugby club" named Blyth Rangers in October 1894.
It appears that Rugby in Blyth would suffer from forming and reforming right up until the 1961 formation, still it would be interesting to fill in the gaps!
For anyone who may be interested the Blyth Rovers first match was against South Shields West End at the Recreation Ground in September 1893. The team that day was:
Full Back: McCormack
Three Quarters: Alder, H.Weyergang, T.Hope, Blackburn
Half Backs: F.Ryder, T.Henderson
Forwards: J.P Isherwood, Jacques, John Hope, James Hope, J.Ryder, G.Robson, J.Aynsley, Walker