Why would they need to ditch their documents if there were more legal and safe routes to enter
That is at the heart of this issue and why so many are driven to desperate measures. So by closing down or severely restricting most legitimate means to claim asylum, the government have actually created a worse problem. If they'd been at all sensible and measured about this, then it could be a real success story for everyone, including our country and economy.
Instead, they've knee-jerked from one crisis or immigration limit number to the next, whilst pandering to/playing on the unfounded fears of those conditioned to think that migrants are simultaneously taking their jobs & house whilst claiming benefits and to those who still in the 3rd decade of the 21st Century, still just don't want immigrants.
A bit less hysteria, a bit less empty rhetoric and a lot more pragmatism from the powers that be on both sides of the channel would go a long way towards making the situation a whole lot better.