Indeed.
Ah poop, I missed out a word! I was arguing that BTL has pushed house prices up. I think it depends on the area though. In the South East I know those four houses would have all gone to individuals rather than landlords if BTL was banned or made to be less incentivised as I know the landlord and I know the sole owner of the 4th house.
If the number of BTL landlords falls, the demand falls so house prices should fall. As the prices fall people move from renting to buying, rental prices should stay the same as there are less houses to rent (increase in monthly rent) but more people move to buy (fall in monthly rent to attract more renters). In all, house prices fall and rental prices stay the same.