Building society Nationwide will pass on the interest rate cut from the Bank of England (BoE) to its tracker and other mortgage customers.
On 4 August, the BoE cut interest rates for the first time in seven years to 0.25%, a record low, from 0.5%, and drew up a £70bn bond buying programme to stimulate the wilting British economy in light of the Brexit vote.
The Governor of the BoE, Mark Carney said that banks has no excuse not to pass on the rate base cut to borrowers.
The building society said that no savings customers on variable rates will see their rate reduced by more than 0.25%. About £40bn of Nationwide's £120bn mortgage book is for base rate mortgage customers, pegged at 2% above the BoE's rate.
Customers who do not use Nationwide's regular savings products will only have a slight cut to rates, as the building society said it will not go below 0.1%.
Chief executive Joe Garner, said: "We will protect members who save regularly and who are building up a deposit to buy their first home."
"We don't want a generation coming through thinking there is no point saving".
There will be no change for customers in Nationwide's Flexclusive regular saver at 5%, regular saver, FlexOne regular saver at 3.5%, help to buy ISA at 2%. There will also be no changes for customers on with the save to buy, and save to buy ISA.
Garner added that following the Brexit result from the European Union referendum on 23 June, the buildings society's focus was on building stability for customers long term.
"As the world's largest building society, we are in the fortunate position to be able to take a long term view and focus on providing great service, security and stability for our members. This will be particularly important in a time of increased uncertainty and market volatility following the EU referendum."
Nationwide follows banks HSBC, Santander and Barclays who said on 5 August they would cut their standard variable rate mortgages in line with the BoE.
The Swindon-based mortgage lender also reported that pre-tax profits ended 30 June rose 6% to £401m and a £368m underlying profit for the quarter.