The scheme, managed by the BBC and infrastructure firm EAGA, is using £603m of licence fee money to enable the elderly and disabled to have a free set-top box installed for £40.
Sky had won a contract to supply participants in the ITV Borders region, the first area to switch from analogue to digital broadcast. However, having installed the boxes, the broadcaster then sent out letters to about 50 people demanding further payment.
A spokesman for Sky said the letters were sent because an administrative error, adding: "As soon as we became aware of what had happened we contacted all of the customers to reassure them that the letter was sent in error."
Sky's apology did not appease Tim Farron, the Liberal Democrat MP for the Westmoreland and Lonsdale constituency who, in a report in The Guardian, described the incident as "appalling".
He told the newspaper: "It's exactly what [people] feared might happen, that Sky would exploit licence fee payers' money to market to vulnerable people."
He claimed that it proved that Sky planned to hold the details of people registered in the scheme on its marketing database.
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