I’ll invite you to consider the following:
The interest rates that lenders can offer on mortgages - and savings products - are determined by swap rates. As a financial institution, you have to make a positive margin between your lending and your borrowing (from savers): if your margin is negative, you’ll soon be out of business.
In practice, the way to achieve balance is by swapping the interest you pay to savers for what was LIBOR (now SONIA : the sterling overnight interest rate, i.e. the rate at which banks lend sterling to each other) and swapping the interest you receive from borrowers, likewise. Swaps can be tradeable assets, although many are bespoke, and their value varies according to both current conditions and short to medium term expected conditions, which can be plotted on a yield curve. What you are doing is e.g. swapping the 3% you’re receiving from borrowers on a fixed rate mortgage, which is the fixed leg of that swap, for x years in exchange for SONIA, which is variable and is the ‘floating leg’ of the swap.
So if someone wants to give you SONIA for 5 years in exchange for 3% on the same (e.g.) £50m you have lent to a tranche of borrowers, it might mean that the other side, the swap counterparty, thinks that SONIA will remain below 3% for a bit and they will get the best of the deal. Or it might just mean that they need some fixed rate interest income at 3% to balance their own margin. Yield curves are notoriously unreliable and are dependent on assumptions. Rubbish in = rubbish out. Two modellers might get very different answers. So the counterparty might have accepted too low a fixed rate in exchange for paying SONIA.
Swap rates change rapidly, which is why you are now seeing lenders’ fixed rates being pulled and replaced with higher rates. That’s because swap counterparties all think that SONIA is heading upwards. The counterparty in the example might have been happy to settle for receiving 3% over 5 years on that £50m but once the £50m runs out, a higher rate is needed to swap for SONIA. So SONIA, and the fixed rates for which it is swapped, don’t always represent long term expectations of where interest rates are going. Banks offer whatever rates they can sell on the swap market in the short term. And, fixes often come with high fees so you’re effectively paying a higher interest rate than the headline rate when you factor in the fee.
Plus, markets are not infallible. The markets expect base rate to be 3% by 2023. The markets didn’t see the credit crunch coming, though. Nor did they notice that CDOs were crap. So I’d be wary of assuming that the banks know everything.