The university later announced it intended the reburial would take place in Leicester Cathedral. Yesterday the alliance called on Justice Secretary Chris Grayling to help determine where the remains should be reburied.
The group's counsel Gerard Clarke told London's High Court the alliance would be satisfied by whatever answer that produced.
The proceedings have been described as "the (legal) Wars of the Roses part two".
Justice Hallett queried whether the right to be consulted applied to "each of the king's ten million collateral descendants" said to be living, Mr Clarke conceded "that would be silly" and said it only applied to those "who may have views".
Battle over where body of Richard III should be reburied is rejoined with Bradford solicitor to the fore From Bradford Telegraph and Argus
Mr Clarke told Lady Justice Hallett, Mr Justice Ouseley and Mr Justice Haddon Cave that the Queen was "silent" on the question of the last resting place of her 14th great grand uncle.
A Bradford solicitor is battling in London to bring King Richard III's remains back to Yorkshire after his undignified resting place was discovered beneath a Leicester car park.
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Legal expert Matthew Howarth, of Bradford law firm Gordons, is representing a group of the king's collateral descendants dubbed the Plantagenet Alliance Ltd which wants the verdict favouring Leicester overturned and the remains reinterred at York Minster.
day judicial review at London's High Court due to end today.
review expert at Gordons representing the alliance, said ahead of the hearing: "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.
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"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.
The fight to bury the bones of last Yorkist monarch in the county Air Max Thea Nike Black has reached the crunch point with a two Air Max 2015 Blue Lagoon
In the unprecedented legal clash, the alliance asked judges to rule that Mr Grayling is under a legal duty to set up a wide ranging public consultation exercise to decide the question.
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