Tesco reductions have been targeted at borrowers with smaller deposits.
The lender now offers a two-year fix of 3.35% for borrowers with a deposit of just 5%, or 2.26% for those at 90% loan to value (LTV).
Both deals come with £250 cashback.
Tesco has also cut five-year remortgage rates at 80% LTV to 2.23%, and 85% LTV to 2.34%, both with £250 cashback.
Leeds doubles buy to let cashback
Leeds has increased its cashback incentives available on select two and five-year buy-to-let mortgages.
The lender has increased the sums from £500 to £1,000.
The range includes a two-year buy-to-let at 2.69% and 60% LTV and without a fee, as well as a five-year equivalent set at 2.74%.
Matt Bartle, Leeds Building Society’s director of products, said: “We’ve increased the cashback incentives available on some of our buy-to-let products while maintaining our product rates.
“Of course, landlords can choose how to spend the £1,000 cashback available.
“Cash freed up at the start of the mortgage could go towards redecorating costs and fees associated with finding tenants.
“Increasing cashback available on our buy-to-let range is a further example of how we’ve used our expertise and experience in the market to understand and respond to the needs of customers.”