Couldn't find it earlier, but the government claim that they will process each asylum application within six months, although it may take longer.
https://www.gov.uk/claim-asylum/decision
It wouldn't surprise me if it wasn't more towards the longer side of things than the shorter side of things. So that's six months where you don't have access to welfare, you aren't allowed to work, and survive on the subsistence money you've either brought with you or are given by the border agency.
You have to imagine it'd help people to assimilate more if that time to process was shrunk a whole lot and they could get on with finding a job. It's probably no surprise that so many turn to black market jobs to support themselves.