Charles Waitt and his partner, Jean Burkin, have been told that the price of the extension will be pounds 1,775.
They must pay the money into the court as the freehold owner disappeared several years ago and cannot be traced. He will be able to claim the money whenever he chooses.
The cost of the extension is based on half the pounds 3,000 difference between the estimated value of their flat in Parkhurst Road, Friern Barnet, with its current 79-year lease, and what it would be worth with a 169- year lease.
The Leasehold Valuation Tribunal, which determined the issue, also added half the value of the freehold owner's interest in the flat's old ground rent.
This was estimated at a multiple of seven times the annual pounds 25 ground rent - pounds 175, which was then halved to pounds 87.50 and rounded up to pounds 100.
Finally, the Tribunal ordered Mr Waitt and Ms Burkin to pay seven years' backlog of ground rent - pounds 175 - to the freehold owner. They had been unable to pay him the pounds 25 annual rent because he disappeared before the couple moved in several years earlier.
The Tribunal decided to value the flat's 79-year lease at pounds 49,000 rather than the pounds 50,000 that Ms Burkin and Mr Waitt claimed it was worth. In doing so, it added pounds 1,000 to the 'marriage value' of the flat - the difference between the value of the property before and after an extended 90-year lease is granted.
This added pounds 500 to the price the couple will have to pay the freeholder. It hints at a tactic now likely to be used by freeholders faced with leaseholders wanting an extension.
Freeholders may try to claim that without a lease extension, their propertyis worth very little. Conversely, they may argue that the property's value would rocket once a further 90 years were added to the lease.
Jennifer Israel, the couple's solicitor, said: 'This is disappointing, given that a person who is currently buying the flat at pounds 52,000 with the lease extension is prepared to pay pounds 2,000 less without it.'
The multiple of seventimes the annual ground rent by which a freeholder's interest is calculated is also relatively low - good news for leaseholders. If ground rents are high and a high multiple of annual rent were used, leaseholders might face a heavy additional bill.
The pric e of freehold ground rents now being sold at property auctions is on an average multiple of eight to 10 times the annual ground rent - which is more than the Tribunal's valuation.
Mrs Israel said: 'The rise in the value of ground rents has partly been stimulated by the leasehold reforms themselves. It would always be open to freehold owners to argue that the multiples should be higher.
'But it is unlikely that tribunals will buy this argument unless a freeholder can prove that this is the case in the area in question.'