Rock star Robert Plant questioned why he was receiving a winter fuel payment from the Government, peers have been told.
Broadcaster Baroness Bakewell said she was stopped in the street by the 69-year-old former Led Zeppelin singer, who she described as a "multi-billionaire rock star".
Lady Bakewell said he wanted to know why he had been sent the annual allowance, worth up to £300 for older pensioners, by the Government.
The Labour peer said the heating allowance for older people should be means tested and when she first received it, she tried to send it back but there was no facility for doing this.
"I, like many, give that heating allowance to charity but it could be means-tested if it was added to the income tax statement of our incomes."
Lady Bakewell was highly critical of the Chancellor for failing more to tackle the controversial issue of social care for the elderly in his recent Budget.
In a debate on the economy, she said: "The Government spends £140 billion on old people. Six per cent of that goes on social care. This is bad economics and bad social care. Will the Government please sort it out."
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