The cuts have been made to two-year fixed rate products between 85 and 95 per cent loan to value (LTV).
The rate for a two-year fixed rate mortgage at 85 and 90 per cent LTV is now 2.29 per cent with a £995 fee and 2.54 per cent with no fee.
At 90 and 95 per cent LTV, the product with a £995 fee has a rate of 3.14 per cent while the fee-free option is priced at 3.39 per cent.
At the same time, the bank has increased rates on its five-year fixed rate remortgages up to 75 per cent LTV by 0.1 per cent. These are the products with a £995 fee and five-year early repayment charge periods.
The option up to 60 per cent LTV has a rate of 1.09 per cent, with rates between 60 and 75 per cent LTV pegged at 1.29 per cent.
The rate changes follow research conducted by TSB which found that over a third of millennials now feel they are less likely to ever own their own home because of the pandemic.
The survey of 5,000 adults also found 27 per cent had seen their financial wellbeing negatively impacted by the health crisis.
Additionally, a third of millennial homeowners said they were now less likely to move to a new property within the next three years. TSB said this could lead to delays in second-steppers making their next moves up the property ladder.
Ian Ramsden, director of borrowing at TSB, said: “Our research shows the concerns that the millennial generation has about getting on to the property ladder.
“The reductions that we have announced today will help some of them take that first step.”