Around pounds 800m is owed to about 80 million people - an average of pounds 80 or more.
The Revenue has already spent more than pounds 7m publicising the new rules, which allow non-taxpayers to register to have their interest paid without having 25 per cent tax taken off.
Around six million people have already registered for gross interest from their bank or building society. These are mainly children, pensioners and married women who have gained their own tax status under the separate taxation legislation.
Clive Corlett, who is responsible for customer service at the Inland Revenue, says: 'We did not expect to find it so difficult to repay money to people.'
A survey conducted last April showed that half those entitled to a refund were unaware that they could claim back tax already paid. The others said they could not be bothered with the paperwork or did not think it worthwhile to claim.
But those who have not yet registered can still get back tax taken off in 1991-92 as well as this tax year.
Some people on low incomes are not entitled to register for gross interest because some of their interest is subject to tax. But they can claim a refund of some of the tax already paid.
The Inland Revenue has found that the elderly are most likely to be confused by the tax rules. So the television and radio advertisements going out concentrate on pensioners.
Some banks and building societies have agreed to carry stocks of a new leaflet, Are You Paying Too Much Tax on Your Savings? (IR 127). One bank, the Midland, has agreed to tell customers about the new leaflet on statements. The Revenue hopes that others will also help to spread the word.
An Inland Revenue spokeswoman said this week that it was finding it difficult to reach non-taxpayers as it did not normally have any contact with them.
The leaflet is also being sent out with more than eight million annual notices of coding to encourage taxpayers to remember whether they know someone who is paying tax unneccesarily.
A more detailed booklet, A Guide for People with Savings (IR 110), gives practical help on working out whether tax is payable on savings.
Income including any pension and interest has to exceed personal tax allowances before any tax is due. The basic personal allowance is pounds 3,445 a year (about pounds 66 a week), with the married couples' allowance or additional personal allowance paid to single parents a further pounds 1,720 (about pounds 33 a week).
Those over 65 get higher personal allowances. A single person aged 65 to 74 can have income of pounds 4,200 ( pounds 80 a week) before paying tax, an older person pounds 4,370 a year ( pounds 84 a week).
The amount owed for the last tax year could easily be more than pounds 1,000 for a married man or pounds 860 for a single person.
Non-taxpayers or those on low incomes can reclaim tax taken off dividend income from shares, but cannot register for gross payment in advance.
The four million people who pay tax at 20 per cent are also entitled to reclaim tax. These people will be earning no more than pounds 2,000 above their personal allowances, yet tax will have been deducted at 25 per cent when only 20 per cent was due.
The Inland Revenue makes those waiting for a reclaim of less than pounds 50 wait until the end of the tax year.
Investors have to wait until interest has actually been credited to their account before they can claim back the tax. Building societies will normally include a note about the interest credited and the tax paid with the annual statement. But most will give investors a tally during the year.
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