As Dr Alf says in this excellent piece from the ONS, they are probably right about falling construction output across the UK as a whole although there are a few exceptions such as Cambridge where the Government is pouring in several billion pounds to create four new mini towns and in the area between Bedford and Milton Keynes.
Overall housing starts have been falling for more than a decade to the present figure of 100,000 a year, road-building has noticeably slowed and further slowing via BREXIT uncertainty will cut construction further.
That plus the Mortgage Market Review, restrictions on buy-to-let lending via insistence on 40% deposits and rising population numbers through people living longer and faster rates of family formation by people already here from certain immigrant communities is going to drive prices up not down and is in fact doing so in London, SE England, the South West where Dr Alf used to live, and in parts of East Anglia away from the impoverished Fens.
Immigrants are needed to plug the gaps in skills of construction and health workers but not in uncontrolled waves of people. The real solution is systems building in factories and a bringing into the 21st century of insurers who refuse to insure non conventional construction, banks/mortgage lenders who refuse to lend on non conventionally constructed dwellings, and reform of local authority planning departments which are mentally rooted in the 19th century. This would require Government action plus the 3D printing of houses which the Chinese and the Americans seem able to do without any imported skilled labour whatsoever.
The NHS and public healthcare needs to be fixed, not by more Indian doctors and foreign nurses, but by taking aggressive action against excessive demand created by malingerers, hypochondriacs, drug addicts, night-clubbers, people fighting at the weekend, benefit recipients trying to get PIP, heavy drinkers, smokers, people with sedentary lifestyles and those who become grossly overweight through eating too much and failing to eat healthily or exercise enough.