You do realise that there's no difference between an illegal immigrant and an asylum seeker other than the illegal asking for asylum? That's how it all works...
No, it doesn't.
'You must apply for asylum if you want to stay in the UK as a refugee.'
Apply for asylum to stay in the UK as a refugee - eligibility, documents you need, how to apply, screening, asylum interview, help you can get, children
Once an application for asylum has been made, that establishes an individuals status. The application then proceeds through the system.
An illegal immigrant has elected to remain outside that system.