Following an advertising campaign, known as ‘Tell Sid’, 425m shares were put up for sale.

Share option legislation was introduced in 1984 by Prime Minister Margaret Thatcher to allow employees and employers to own shares in formerly state-owned companies.

Shares were allocated free to workers with the option to buy more at a later date. As a result, by 1987 some 20 per cent of the population were shareholders, up from just seven per cent ten years earlier.

While many shares were sold straight after, those who kept them could now be sitting on a significant profit.

Simply Stockbroking says that someone who bought the minimum amount of 100 British Gas shares for £135 in 1986, could now be worth £1,686.

John Douthwaite, chief executive of Simply Stockbroking, said: “Millions of people will be sitting on share certificates issued in the 1980s, which will now be worth a considerable amount of money.

“May have shied away from selling largely due to ignorance or fears of brokerage fees eating into profits from the sale, others may have inherited the shares and simply forgot they had them.”