The LSE's figures commissioned by the Mayor show that there are around half a million illegal immigrants in London alone (midpoint). I've yet to read the actual report, but the Mayor's news release was very specific - the figure was just illegal immigrants. So presumably it doesn't include asylum seekers, east Europeans or other EU citizens, or all the Nigerians having babies. Boris is in favour of an amnesty. More reasoned voices on both sides of the political spectrum have pointed out that what starts as an amnesty ends with a truckload of dead Chinese.
Illegal immigrants take bedspaces and rented accommodation and crowd out rented property availability. By their nature they swim in a world of illegality and criminal activity, victims and perpetrators both, and allow more serious and organised crime to flourish. By working for below open-market wages, they create opportunity costs in lowered GDP and continued welfare costs for non-illegals. In every way, they damage our society and economy.
There is only one answer; greater control of our borders, and accelerated removal. The UK isn't just a hotel that the world's poor can choose to book into; it's our nation, and it runs on our taxes. And it's about time we shut the door.