Halifax, Britain’s biggest mortgage lender, is planning to reduce the cost of its best tracker deals - but only for those borrowers who can afford to put down deposits of at least 40 per cent.

Two and three-year tracker deals, with a starting rate of 5.99 per cent, are part of a wider revamp of Halifax’s mortgage range and will move to further alienate first time buyers.

The bank is not revealing details of the changes until Friday, but a note sent to mortgage brokers, and seen by The Times, shows it will be introducing two and three-year tracker deals at 0.99 percentage points over base rate, currently 5 per cent, with a £999 arrangement fee. But the deals will be available only to those borrowing no more than 60 per cent of a property’s value.

Halifax is also cutting the rates on its three and five year fixed rate deals for those borrowing up to 75 per cent of a property’s value. Its five-year rate comes down by 0.35 percentage points to 6.09 per cent, while the three year rate drops by 0.22 points to 6.22 per cent.

While the bank is cutting rates for its least risky customers it is raising loan costs for some borrowers with small deposits.

Those needing to borrow between 75 per cent and 90 per cent of a property’s value will pay more on a three-year fix. Those moving home will pay 6.64 per cent while those remortgaging will be charged 6.89 per cent. All these fixed deals will also carry a fee of £999.

A Halifax spokeswoman said: “We are focusing on rewarding customers for their prudence.”

Melanie Bien, of Savills Private Finance, a mortgage broker, said:, “We are delighted to see a number of rates coming down though some borrowers with only small deposits will have to pay more for their home loans.”

The bank’s move follows increases in fixed rates by rival lenders in recent weeks. Abbey has raised its fixed rates on some deals by 0.26 percentage points, Nationwide and Woolwich, the lending arm of Barclays, have lifted their fixed rates by up to 0.3 points while Bradford & Bingley is charging up to 0.55 points more on its fixed deals.