This is now worth more than pounds 270 but people who had mortgages and savings accounts with the Abbey would be entitled to shares worth twice that.
Abbey's articles of association allow it to start disposing of the unclaimed shares from this weekend. The Abbey was the first building society to convert itself into a publicly quoted company, and at the time it wrote to all savers it believed were eligible to receive free shares.
It is thought that many of those who have never come forward had changed addresses and never notified the society. Some will have died, and some may have refused to claim their shares because they were opposed to the idea of the conversion.
In the case of those who have died, Abbey says that providing the deceased was eligible for the shares in the first place and died after 15 June 1989, their estate would be able to claim. They will be sent a form and invited to register for eligibility. The bank will have to check this against its own records, and John Fry, group services director, said this could take two or three weeks.
In addition to writing to the 390,000 mystery share owners, Abbey will also be advertising in national newspapers on 20 July. Three months after that it can start selling the unclaimed shares, although Mr Fry said the company would be in no hurry to do this.
Claimants must fill out a form for their shares, and although they can obtain one by telephoning 0500 500 202 they must complete the paperwork. Forms are also available in Abbey's 700 branches.
Although Abbey will be selling unclaimed shares, people coming forward within six years of the sale will be able to collect the proceeds plus any dividends declared until then. Also, they remain entitled to dividends declared before the sale for 12 years after the declaration. So far, dividends of 25.7p per share have been paid.Reuse content