This was the question posed recently on the excellent mremag - the thrice weekly supply of news and views for railway modellers.
I suspect that as the oldest model railway club, our first exhibition is probably the first - in which case the answer would be March 13th 1912 as one of our club evenings that was also open to the public. The first two day show was at the Kingsway Hall in Holborn in 1924. It's timing over the Easter weekend led to the start of the traditional London Easter show. With the changes in working and holiday patterns, Easter isn't such a good time for a London show, so the equivalent event - the London Festival of Railway Modelling takes place at the end of March each year, in which the MRC is proud to play a key part providing the 'amateur' content of the shows.
There's more detail in the MRC's centenary supplement from BRM - which you can read here.