Immigration is not the cause of the housing shortage and the problem is older than 10 years.
The wave of Eastern European immigrants have not bought houses here (they are usually in rented accomodation) so their presense has had no impact on the housing market.
The main cause is very simple. There are not enough houses being built. And a massive increase in singles dwelling. As we have become more affluent, we can now afford to buy houses/flats on our own. And has been said earlier, we are living longer.
4 is incorrect. Wage rises are usually pegged to the inflation rate which is now conveniently adjusted not to include house price rises. The result will be that rather than get morgages and wages will rise, people will instead be priced out of the market.
5 We are not approaching economic meltdown as you seem to be implying. Infact we are doing very well economically.
Can we carry on like this? - No.
With first time buyers and the low paid effectively priced out of the market, the market will diminish in the long run. That is not to say the need for houses will diminish, just that the number of people who are able to buy will decrease.
More houses will need to be built.