What is a bogus/illegal asylum seeker? There is no such thing! Anyone may claim asylum under the Geneva and Hague Conventions.
That claim may fail for all sorts of reasons, eg. lack of documentation for British Army interpreters pre 2013 in Afghanistan. If it is safe to do so a failed claimant will be returned to his/her country of origin.
Who decides their claim?
At first this is decided by a case worker at the Home Office. They do not have any legal training. If they reject a claim, only then can an asylum seeker appeal to a tribunal. Often a rejected claim will be allowed.
What happens to a failed asylum seeker?
If it is impossible to return a failed asylum seeker to his/her country of origin, either because it is unsafe, eg. Syria, Afghanistan, or because that country will not accept them, then they become destitute. This means they lose the accommodation supplied by the Home Office, the subsistence allowance, health care, educational courses.
They do not have the right to work. Often they live on the streets, unless a friend takes them in.
If they have children, basic housing may be supplied together with a subsistence card ("Azure card") with £35 per week available for basics such as nappies and food.