Buck ,

I thought at first glance that It might be a variation of the BSA light sporting rifle they made in .300 Extra Long (i.e. Sherwood) and .32-40.

That however used a Lee Enfield bolt in a simplified tubular receiver as did their .410” single shot.

Yours has a front locking bolt.

X01 appears to be someone’s (not necessarily BSA’s) prototype serial.

My guess is that the inventor of the action started with a .22 BSA War Office Pattern barrel and bored it out to take the .310 Cadet cartridge, then fitted it to his prototype action and modified the stock to fit.

I do not recognise the action and the P(ending) Patent mark does not necessarily mean that it was ever Patented.

It might have been made at Lithgow in Australia as the .310 Cadet was popular there.

The Australian government started producing FMJ .310 ammunition for Home Guard combat use when Japanese invasion seemed imminent.