Nottingham Building Society is cutting mortgage rates and improving criteria this week, while Leeds Building Society is lowering some prices and increasing others.
At Nottingham all standard residential rates for new customers are being reduced on Friday.
The price cuts are up to 21 basis points.
Nottingham has also eased criteria across both standard residential and foreign national new business lending this week.
It is now offering loan-to-income (LTI) multiples of up to 5.5x on gross incomes of £60,000 and above across all loan-to-values (LTVs) and purposes of mortgage.
The building society has also begun accepting family visas as part of its Foreign National range and simplified rules on the minimum amount of time borrowers must have been with an employer.
At Leeds Building Society, a number of residential fixed rates for new customers will drop by up to 17bps tomorrow and Right to Buy rates by up to 15bps.
But at the same time it is increasing some of its First Homes fixed rates, although it has yet to specify by how much.
For existing borrowers, some buy-to-let and portfolio buy-to-let rates will fall by up to 15bps and some residential fixed rates by up to 7bps.
Other lenders to cut rates this week include Halifax, BM Solutions, Accord, Barclays, TSB, HSBC and Principality.
It comes as Moneyfacts revealed that low-deposit mortgages are at their cheapest point for three years and the average two-year fixed across all LTVs has fallen by 45bps over the past year.
