Why not get your tourist Visa in as a holiday, pay for your cheap flight then say you've arrived on small boat? So you get your "asylum" claim like the rest of the lot put up in hotels etc?
A lot of people do exactly that. This is part of the problem, people seem to be under the impression everyone is turning up in small boats which is far from the case.
Of course this is only possible when coming from a country where you can apply for a visa, the government are also in the process of restricting visas issued to people coming countries they view as at risk of overstaying or claiming asylum once here.
A large number of people who overstay visas don't actually apply for asylum, they just disappear into the cheap labour, cash in hand market.