Rents are included in the basket of items for CPI. Mortgage repayments and interest rates aren't.
The thing is, all prices are "weighed" if for example, (I'm pulling these numbers out of thin air) the average household spent 20% of their wage on rent, and rent goes up 10%, then they multiply 10% by 20%, and it increases CPI by 2%.
And the result is not generally a direct feedback. I trust you haven't passed on every single rate rise onto your tennant have you? That's why it's important that the media and government don't go for the beat up "Landlords had better not raise the rent too much". Because when occupancy falls, Landlords must drop rents or accept a vacant property, regardless of where rates are going. Therefore, if they do not take the opportunity to put up rents when they are high, landlords are basically being shafted on the way up and on the way down.