I dont think it is correct to assume rents increase with interest rates. If interest rates rise, market prices adjust to maintain mortgage payment affordability. So prices should theoretically come down, hence mortgage repayment for an incoming investor should affect the rent he/she is prepared to accept.
Now for existing landlords this may be different depending on when they bought and how much debt they have. Highly indebted investor will have to compete with incoming landlords and existing landlords with low debt.
If rental supply is adequate or inexcess of demand there is unlikely to be any scope for landlords to raise rents, even if interest cost rise.
