Arthur George owns 12 seats in two separate boxes, and William and Alexander Stockler together own four seats in one box.
They asked the judge to rule in their favour without a trial and award an interim payment of £500,000 in damages, ahead of the full amount being decided, which was opposed by lawyers for the RAH.
In a written judgement on Tuesday, the judge dismissed the bid and said: “It would seem to me to be potentially unhelpful to have the declaration sought.
“Whether any declaration at all is justified at a trial, when all the relevant issues and defences have been canvassed and ruled on, will be a matter for the trial judge.”