https://www.homeless.org.uk/facts/homelessness-in-numbers/rough-sleeping/rough-sleeping-explore-data
Looking at the figures above, this would in practice mean housing for fewer than 80 people per region (with the exception of Westminster, Brighton and Cornwall). This is hardly going to devastate the property market.
Rough sleeping is, furthermore, something that only the government really has the ability to do anything about. Charities like St. Mungo's or the Castle Project cannot command the resources to run property - certainly not to increase the limited accommodation they already have - in anything like the required numbers, however excellent those services are. Private philanthropists are also not forthcoming on the issue, so there isn't really another alternative but to a) let rough sleepers continue living on the street or b) have the government do something.