In May, first-time buyers had to borrow 3.37 times their incomes to afford a mortgage, while other movers had to borrow 3.03 times.
Due to the rising interest rates, interest payments for first-timers took up 19.1% of their incomes, the highest percentage since 1992. Other home movers saw interest payments taking 16.6% of their incomes.
CML's director general Michael Coogan said "For anyone wanting to get a foot on the property ladder or move house, each month, affordability is becoming worse. Today's data does not take into account either of the 0.25% rate rises in May and July - so it is inevitable that affordability pressures will become even more pronounced in the coming months," he added.
With interest rate still set to go higher fixed-rate mortgages are still proving very popular.
The CML said that 89% of first-time buyers and 73% of home movers took out a fixed-rate deal in May, which was up from 88% of first-timers and 72% of other house buyers in April.
In spite of the 5 interest rate rises since last summer, house prices in the UK have continued to rise steadily and are now 11% higher than they were a year ago.