George Osborne will reject growing demands by Conservative MPs for significant tax cuts for the middle classes in his Budget next Wednesday.

The Chancellor will argue that it would be fairer to target any tax reductions on people on lower incomes. He is expected to announce that the personal tax allowance, which will already rise to £10,000 a year month, will increase to at least £10,500 in April next year.

His decision will disappoint Tory MPs, who are pressing for lower taxes for people who have been sucked into the 40p rate, which starts to bite on incomes of £41,866 a year from next month. Yesterday the backbenchers won the backing of two former Tory Chancellors, Lord (Nigel) Lawson and Lord (Norman) Lamont.

Download the new Independent Premium app Sharing the full story, not just the headlines

The starting rate has been frozen or reduced in recent years in order to fund the decision to take lower paid people out of the tax net. But this has drawn more taxpayers into the 40p band as their incomes rise. When Lord Lawson introduced it in 1988, about 1.35m people paid it. Today 4.4m are in it and the number is forecast to reach 5m before next year's general election.

David Cameron and Mr Osborne are to launch a drive to persuade Tory MPs that it would be wrong to spend scare resources on reducing taxes for people on middle rather than low incomes. They will warn that raising the 40p threshold would mean that people earning between £42,000 and £50,000 a year would enjoy tax cuts twice as big as those for someone paid £20,000.

Ministers will also repackage the increase in the personal allowance as a measure that helps all taxpayers earning up to £100,000 a year, not just low earners. One senior Tory MP said yesterday: "It does help the middle classes, but we haven't 'sold' it properly. We have presented it as helping those at the bottom of the income scale."

As part of the fightback, the Treasury will issue figures showing how people on the 40p rate have shared the benefits of the rise in the personal allowance because they pay tax on a smaller slice of their income. A typical 40p rate payer will pay £164 less income tax and national insurance (NI) in the 2013-14 financial year than in the previous year. In 2013-14, such a taxpayer's tax and NI bill would be £350.50 lower than in 2010-11, rising to £504 next month.

Treasury statistics also show that someone on £40,000 is £431 a year better off than he or she would have been under the tax and NI plans of the previous Labour Government. A person on £43,000 is £276 a year better off and someone on £44,000 is £176 better off.

Ministers fear that raising the 40p rate threshold could damage the Tories' electoral prospects by provoking Labour claims that Mr Osborne was pandering to his party's supporters rather than helping those most in need. Labour branded the Tories as the "party of the rich" after Mr Osborne cut the 50p top rate on income over £150,000 a year to 45p last year.