London's mayor, Boris Johnson, who is responsible for the capital's policing issues, has been ordered to meet compensation claims of almost £75m for the destruction of a Sony warehouse during the London riots of August 2011.

Describing the fire as reputedly "the largest arson in Europe", three appeal judges headed by the master of the rolls, Lord Dyson, dismissed Johnson's challenge, to an earlier ruling, which referred to legislation first passed 300 years ago.

Last year, a high-court judge ruled that insurers, and the owners of uninsured property, were entitled to compensation from the mayor. They had claimed more than £62.8m.

In upholding that ruling the appeal judges have now gone further and said the mayor is also liable for consequential losses, such as loss of profit and loss of rent. Those figures were put by the claimants at £11.4m.

Sony and the warehouse owners had previously made successful claims against their insurers. Those insurers brought claims under the Riot (Damages) Act 1886, which says that compensation for damage caused by riots must be paid for by the police fund for the area.

Recent legislation covering the Metropolitan police district lays the responsibility for paying compensation at the mayor's office for policing and crime – a corporation of which the mayor of London is the sole member.

The mayor's office had argued that the disturbances were not covered by the 1886 act. His lawyers were refused permission to appeal to the supreme court, although the mayor could ask the court itself to grant permission.

Unless the judgment is reversed, the money now owing to the insurers will have to come from public funds.

The trial judge, Mr Justice Flaux, said last year that that the Sony distribution warehouse in Enfield had been destroyed and looted shortly before midnight on 8 August 2011 during "the widespread civil disorder and rioting which took place in London and elsewhere". The disorder followed the shooting dead of Mark Duggan by police in Tottenham, north London.

Flaux said the attack on the warehouse was "perpetrated by a group of some 25 youths" who had earlier congregated at a nearby housing estate.

He added: "Two of them then threw petrol bombs into the stacking within the warehouse and they all made their escape, some carrying what had been looted, and left the warehouse to burn.

"The whole incident took no more than just over three minutes. However, the fire took hold and burned for some 10 days, with the total destruction of the plant, equipment and stock."

Giving judgment in the court of appeal, Lord Dyson, Lord Justice Moore-Bick and Lord Justice Lewison said it might seem "surprising that the community should be under a strict liability to pay compensation for the consequences of riotous and tumultuous behaviour at all, when the police are not liable in tort for such consequences even where they have been seriously at fault".

However, the judges continued, this had been the law since 1714 and only parliament could now alter it.

The Riot Act 1714 (from which we get the phrase "reading the riot act") provided for compensation if persons "unlawfully, riotously and tumultuously assembled" demolished buildings. In the case of property within a town, the compensation was to be paid by its inhabitants, if necessary through levying a rate.

Explaining the policy behind the 1714 act some 60 years later, the well-respected chief justice, Lord Mansfield, said the idea was to encourage local residents to suppress riots.

Mansfield said it was a "very ancient principle, as old as the institution of the decennaries by Alfred, whereby the whole neighbourhood or tithing of freemen were mutually pledges for each other's good behaviour".

The main change made in 1886 was to transfer liability from the inhabitants to those who paid police rates in the district where the property was situated.

Even if this were considered "unfair and unwarranted in the 21st century", the three appeal judges said on Tuesday, "it is for parliament and not the courts to amend it or remove it altogether".

Last year, the government published the recommendations of an independent review. David Wilkinson, a partner at the law firm Kennedys, who acted for Sony's insurer, Royal and Sun Alliance, called the ruling a landmark decision.

He said: "Insurers and uninsured claimants will now be able to recover business interruption losses suffered as a result of the London riots. However, whether each and every claim will be ultimately paid remains to be seen."

The doubt, he explained, was due to the compensation authority being entitled to take into account all the circumstances –including the conduct of claimants and any precautions taken by them – before fixing "such compensation as appeared to them to be just".

The mayor's office for policing and crime said it noted the judgment from the court of appeal and was "considering potential next steps in the legal process".