The cost of mortgages is not dependent solely on the base rate. It's dependent on the price the market demands for lending you money.
That is a complex function of things like default risk (the fact that you might not pay), inflation (that the money paid at the end of the loan will not be worth as much as it was at the beginning) and margin (how much money the intermediary for the debt wants in reward for risking to lend to you).
Back in the good old days when mortgages largely tracked the base rate a rise in the base rate was reflected in the price of the mortgage instantaneously.
Now the price of a mortgage more reflects the cost of taking on debt at any particular time.
The 2 year and 5 year gilt yields are a reasonable proxy for 2 and 5 year mortgage rates (there are better ones, called swap rates but these will normally do). These are the yields the market charges to lend the government money for those periods. The government can borrow money at less cost than a mortgage owner because it is considered more reliable (hence the lower yield on the 2 and 5 year gilts compared with mortgage rates), but still, the yields tend to move in harmony.
The 2 and 5 year gilt yields spiked around 10 July, but have dropped around 10% since then to now (about 0.5% or so), so it is reasonable that the mortgage rates will have dropped somewhat since then as well.
if you take the 0.25% base rate rise that will almost certainly happen tomorrow, that could be interpreted in two ways :
i) the government is serious about reducing inflation by increasing the rate. 2 year gilt yields will go down, because investors are more confident the money they will get back at the end of the loan period will be worth more - mortgage rates go down.
ii) the government is not serious about reducting inflation because it hasn't increased the rate enough. 2 year gilt yields will go up because investors are worried that the money they will get back at the end of the loan period will be worth less. Mortgage rates go up.
There's more to it than this, but these are some basics that show how the base rate can increase while the actually mortgage rate decreases.