Their margins are 30% on new builds, even higher on new build flats. They will still make profits, just a little less.
Market value depends on what people are willing to pay. If nobody can pay, say £1500 for a flat. It doesn't matter whether the costs to the landlord is £1000 or £5000, the market value is still what someone is able to pay.
We are always at that ceiling, because if there were any headrooms the landlords would already be charging more. Landlords don't leave money on the table waiting for their costs to go up before increasing rents.
The only time rents increase is when people bring in additional money to pay, not when landlords have additional costs. When we had wage growth and low inflation, there were additional money to pay. Interest rates were going down for a decade, did rents go down? No.
The rental market is not that liquid. If you're a landlord and have a rent paying tenant paying £1000 and you want £1500 to maintain your previous margins, evicting them means months of nobody paying any rent and you searching for a tenant that may or may not exist. If tenants stop paying the landlords can't find someone who pays immediately. If house prices do drop then there would be new landlords buying properties who have a lower mortgage, and are able to undercut you on the rent.
These stuff are not theoretical, the concept is very well studied. Rents don't follow interest rates, you can plot rents and interest rates and see no correlation. Rents generally follows wage growth.