Illegal immigrants in terms of visa overstayers are not usually a great burden on this country which is why the government bothers doing very little about them.
They cant claim benefits, sure they can’t pay income tax or NI and often work cash in hand but then they are buying goods and services, paying VAT and council tax etc .
They are charged for NHS use but often can’t pay however this means they tend to be low level users because it brings them into the system and they are looking over their shoulders all the time re the risk of deportation. They do use schools if they have children.
Ive worked with a few families who were here illegally and their existence was very fragile, they were exceedingly low income (not top up benefits) and had no recourse when an employer was unreasonable. Fired during pregnancy? Working 90 hour weeks? No real options, except quit or put up and shut up
Become unwell? no recourse to benefits, push through or be deported. They’d be back at work a week post birth leaving the baby with a non registered childcarer.
They lived in one room with three kids, landlord kicked them out (and they did often) no recourse to accommodation, you find someone to stay with or risk deportation. Mouldy, unsafe housing? Not many options except hope to find somewhere else. Renting in the system is hard without evidence of non cash in hand employment so your chances of a dodgy landlord have gone way up.
If you’re reliant on legally resident family, better not upset them.
In London especially there are many families and probably many more single people living like this. When things go well it works but add in illness, injury, a pregnancy, a row with family and the fragile existence becomes untenable. What is really interesting is that many people consider this better than life in their home country.