The reason ilegal imigrants are cheap labour are because they dont pay any taxes on their earnings. In the recent UK general election Lib Dems had a policy over an imigrant amnesty. All imigrants would be granted citizenship and then be eligble for National Health Service and social benfits but would also have to pay tax. This would generate additional revinue to the economy as well driving out the market for cheap labour. Each imigrant would have a permit entitling them to work in a certain area of the country and employers would be fined if they were caught employing people without the right paperwork. Interesting idea.
Someone reading your post would think that those illegal immigrants are taking advantage of not paying taxes and living a comfortable life.
In the UK healthcare is free due to the NHS being funded from our taxes therefore we do not have health insureance.