As Rascal mentioned earlier I think it's more likely that government investment hasn't kept up with population change as opposed to there's just too many people. Right now the population is only growing by around 0.4% per year, how can we not cope with that? The problem is the government will spend over £1trillion publicly this year and you'd struggle to figure out what it actually gets spent on.
Either way the trajectory of the population shows that we're slowly approaching a point where the population will start to reduce because our birth rate is very low and our death rate is higher. The only bridge between that is immigration and with the birth rate staying as is we need more immigration and not less. We haven't got an aging population, we have a population that is skewed by people living longer who are having less children.
Now some would say that a falling population might be a good idea but it's actually bad because it's impossible to grow as a country if the population starts to fall. Most starter and less skilled type jobs for example are worked by young people and it's a bit difficult filling those jobs when there are no young people. The taps have also been closed to the EU so we're going to see big problems in the labour force as there just aren't enough people.
Back in the baby boomer days it was traditional in a couple for the mum to stay at home to look after the kids, that's mostly impossible today because of the finances involved. If we are going to shut off to immigration then we really need to look into helping young people to have more kids. By that I mean we need to help them into affordable housing and they need help with childcare and better paternity/maternity benefits.