Mr Justice Latham granted the families leave to seek court orders quashing the jury's verdict of unlawful killing, given yesterday. The case is likely to be heard in London in the next few months.
The two-day inquest at Brighton had been told that Trevor Carrington, 38, an unemployed airline steward, had confessed to starting the fire on 18 April as 'a prank', then two days later threw himself under a lorry.
The families had earlier walked out of the inquest in protest at the refusal of the East Sussex coroner, Dr Donald Gooding, to call a property millionaire, Nicholas Hoogstraten, as a witness to ownership of the flat, which had no fire escape.
At a 15-minute private hearing in London, Mr Justice Latham ruled that the families had an arguable case for judicial review of the inquest on the basis that the coroner acted 'unreasonably and unlawfully' in refusing to call Mr Hoogstraten.
On the first day of the inquest, Colm Davis-Lyons, representing the families, had told Dr Gooding that there was evidence identifying Mr Hoogstraten as the probable leaseholder of the three-storey building.
But, after examining the dossier offered by the families, Dr Gooding said that he could find 'no firm evidence' of such ownership.
The inquest was told that council officers had immense difficulty finding out who owned the building, and ownership changed more than once between 1988 and 1992, so that they were unable to persuade anyone to comply with local instructions to install a fire escape on the upstairs landing, which might have saved some lives.
The latest national guidelines for buildings converted into flats do not recommend the installation of such fire escapes.
The freehold of the building has subsequently been bought by one of the occupants, but at the time of the fire was owned by De Alnie, a company registered in the British Virgin Islands. The offshore registration means the names of the company's directors are not open to public scrutiny.
In his summing-up to the jury, Dr Gooding said: 'There can be no doubt that, if a fire escape had been present, fewer people might - and I stress might - have died, but at least they might have had a chance which was denied to them.'
The five who died in the blaze in Palmeira Avenue, Hove, were: Andrew Manners, 29, of Cheltenham, Gloucestershire; Mabel Smith Roberts, 46, of Colwyn Bay, north Wales; Timothy Sharpe, 28, of Palmeira Avenue; Paul Jones, 33, of St Michael's Place, and Adrian Johns, 32, of Richmond Place, both Brighton.