The Plantagenet Alliance Ltd, formed by the distant relatives of King Richard III, are fighting for the late monarch's remains to be buried at York Minster, claiming it was the king's wish.
They are bringing judicial review proceedings against Justice Secretary Chris Grayling, the University of Leicester - which intends to bury the remains at Leicester Cathedral - and Leicester City Council.
Their solicitor, Matthew Howarth, from law firm Gordons, said:
Quite why our opponents have declined the obviously sensible option of independent adjudication, preferring to incur substantial legal costs - including for the taxpayer - and tie up considerable court time, is inexplicable.
Although many people are astonished we've got this far, we'll go to the hearing with every confidence in our position, intending to state our case clearly and believing there's every chance the licence will be quashed.
If that happens, the odds about the king eventually being laid to rest in York will shorten dramatically.
At the heart of the case is a Ministry of Justice decision to grant a "section 25 licence" under the Burial Act giving archaeologists from the university licence to excavate, and the university permission to decide where to re-bury the bones, which were exhumed in the city 19 months ago.