My worry is that a day will come when rents start to increase. My great fear is that this will happen precisely when interest rates are high. What will we renters do then? We will truly have no choice then. The housing market in the UK is going through something like this now.

They're not going to raise interest rates in the teeth of a housing crash. You're going through exactly what I went through where I live, and I was able to pick up a house for half what it would have cost if I bought when I moved here.

The previous owner bought at the peak and still owed double what I paid. Don't be that guy.

Interest rates in the UK are 0.5% and have been for 7 years now. These low interest rates, while necessary for the real economy with inflation near zero, support extremely high house prices. Mortgage interest payments substitute for rent so low rates imply high prices.

As a renter without much in the way of assets a high inflation high interest rate regime is really beneficial. Higher rates would mean lower prices (thus lower required deposits) and high inflation would mean quickly building equity.