Right let's look at the figures.
Spud says our population density is 407 per square km. Let's take that at face value. Current EU immigration is about 170,000 people per annum. That means that, in 10 years there would be an extra 1.7 million people if it stayed that way. That's about a 2% increase in the current population. So for each square km there would be an extra eight people.
Or, in schools (assuming no new ones are built) a class of 30 might become a class of 31 or might not. If you go to A&E and there are 50 people there, in 10 years there would be 51.
Is really such a big deal? No, it isn't. The immigration debate has been whipped up out of all proportion to the size of the actual problem and it has been done so to frighten Little Englander into making a bad decision in the referendum.
You didn't add non-EU migration which adds another 100,000 + to the net figure, and population growth due to birth rate exceeding death rate.
According to this,
https://en.wikipedia.org/wiki/Demography_of_Englandthe population of England has doubled in the last 125 years.
Since 2006, net immigration has been significantly higher than before 2006.
In or out of the EU we probably won't stop the population increasing. If the world population goes up, so will the UK's.
However, if we take the approach whereby we build more in order to accommodate more, fields that we see from our windows now will one day be gone, and the country will become less and less able to support itself in the event of a crisis, since the source of our food is fields.