Anyone who is in the Uk illegally is probably keeping a very low profile and working for peanuts in a horrible job, and living in constant fear of being sacked and having no support at all. If you are not legally here, you can get no benefits, no health care, no schooling for your children, no ante-natal care, nothing You do not exist.
Asylum seekers and legal immigrants, on the other hand, have applied to live here as soon as they arrived, or as soon after as they could, and have either eventually received permission after jumping through all the hoops or are going through the miles of red tape needed. Here is the procedure, from the horse's mouth. www.gov.uk/claim-asylum