Unless there is a working reliable SLR ready for development/mass production then then sorry but no there was nothing ready or good enough when the decision has to be made.
The purpose of the No4 was not to provide a better rifle per se but to provide one that was better suited for then modern mass production techniques
The Garand for example was not properly ready for mass production until the war had started and even with the exceptionally good US production rates it was not being produced in nearly enough quantities until 1943 and other SLRs of the war were not as good.
That all being said I have always considered the early Dieudonne Saive SLRs such as the weapons that became the FN40 that eventually became the FN49 as a possible SLR that the British could leverage in the late 30s in order to produce an 'No4' SLR ready for production before WW2.
Obviously this would require the purse strings being lossened earlier and a great deal of investment in the late 30s.
Couple this with a switch to 7.98mm (which would include the BREN/ZB30 and adopting the ZB53 MMG as a infantry weapon as well as an AFV weapon) and we might see improved development of the BREN as there would be less development in switching it to 303.
Of course the risk is that the British are caught changing horses at the start of the war and it would leave the commonwealth nations still using 303 SMLEs and pose the issue of mixed calibres - that being said small arms represented a very small slice of a given units daily logistics and I don't think it would have been as big an issue as some people seem to fear.
I wrote a little story on this a few year back
en.wikipedia.org
