Set up: A lot of buy-to-let landlords are highly leveraged. Interest rates jump up. What do you rationally expect?
I expected that with IR up, monthly payments for the landlords are up. They can't afford the payments, they sell (presumably to live-in buyers). Selling pressure means prices go down in the near term.
Instead what's been happening for at least a year is that the landlords have been putting rents up. This works for as long as renters are willing to pay up. There's less and less reason to, though. Also, it's normally not enough for buy-to-let landlords not to take losses, so basically they're just betting they can take smaller losses fora a while and it'll all go "back to normal".