The United Kingdom is currently in the process of exiting the EU. This process should be completed by 1st January 2021 (although there have been suggestions that this date could be postponed due to the impact of COVID19).
Under current proposals, EU nationals who are not eligible to use the existing EU Settlement Scheme (EUSS) will be subject to the same immigration criteria as all other nationals. These will be updated to reflect what the government perceives as the UK's current needs.
The proposals in brief
Immigrants who wish to work in the UK will need to score a minimum of 70 on a points-based system which assesses their ability to speak English, their overall education, whether or not they have a job offer and if so at what salary and whether or not they are in a "shortage occupation".
At present shortage occupations include roles in agriculture and the NHS, but not in construction (or logistics on which the construction industry depends heavily).
Immigrants who wish to study in the UK will be assessed similarly but points will be awarded differently. Potential students will need to show that they can speak English, have an offer from an approved university or college and can maintain themselves during their studies.
The impact on construction
Not only has the construction industry become heavily-dependent on EU workers, but it is also dependent on other industries which are likewise heavily-dependent on EU workers, for example, the haulage and logistics industry.
If this reality is not recognized in law, then there is likely to be a severe slowdown in construction.
This slowdown might well be temporary. For example, the government could train UK workers and/or encourage the domestic manufacture of the necessary materials.
It is, however, hard to see it lasting any less than a few years (at best) and it's also hard to see how the government could meet its home-building targets during that time.
The impact on landlords
There are two main ways in which the immigration system could impact landlords. The first is by reducing demand. On the whole, however, there is so much demand (and so many investors leaving the buy-to-let sector for various reasons), that this is likely to be a fairly minor issue.
The second is the need to conduct Right-to-Rent checks lawfully. This, however, is very much a "watch-this-space" situation as the concept of Right-to-Rent is being challenged in the courts.
The impact on home sales
If construction slows down then the volume of home sales will also slow down, because there are fewer homes to sell. If demand slows down at a similar rate then there should be balance.
If, however, construction slows down significantly, but demand only slows down moderately (if at all), then the UK could easily end up in a situation where there is high demand but low supply.
In principle, this could lead to a sellers' market with rising prices. In practice, however, most buyers in the UK need mortgages and mortgages reflect what the lender thinks a buyer can afford.
This could create a situation in which owners of larger properties, such as family homes, cannot sell their properties for a price which justifies downsizing and hence choose to stay in them, thus creating a bottleneck in the housing market.