I think they must do the same in WSL (hence what I've seen referenced above). I've run down from Burgess Hill a couple of times but always managed to bring a small enough rucksack to take in............
I'd give Supporter Services a call to be sure - they're always helpful. The below link isn't clear on size of bag allowed. I've seen a few people trying to get in with bags before and they've been told it needs to be held until after - always appeared as though there was a storage area near the...