Mortgage rates do not go up equally at the same time. They did in the days of 25 year variable rate interest mortgages, but not now.
How much any mortgage payment will go up will depend on the mortgage rate when the mortgage was negotiated, how long the fix was for and what the rate will be when it needs to be renegotiated.
Assuming that most mortgages are repayment mortgages, it will also depend on how far through the overall 25 years length of a mortgage you are.
Monthly mortgage payments are a mix of interest rate and capital repayment and to keep the monthly payment even, in the early years each monthly payment is nearly all interest with only a small amount of capital paid back, but this changes as the mortgage progresses and by the time you reach year 20, most of the monthly payment is capital repayment, a figure falling fast and the interest payment proportion is quite small.
So if 2 people both have £100,000 mortgages, currently paying 3% interest, due to go up to 6% in September but one is in year 2 of their mortgage, while the other is in year 22 of the mortgage, the person in year 2 of their mortgage will face a substantial rise in their monthly payments because with so much capital still to be repaid, the interest payable on nearly £100,00 will be high.
For the person in year 22, they will probably have repaid at lest half their mortgage, probably 60%, £60,000, so the new interest rate will be calculated on the £40,000 capital outstanding, which will be much less than the interest on nearly £100,000 the person in year 2 of their mortgage will pay, so the second person's interest payment will go up, proportionately much less, and this will affect their overall household budgets much less.