Lord Justice Leveson's letter responded to Conservative MP Rob Wilson, who had demanded the judge examine the relationship between Carine Patry Hoskins and David Sherborne.
Mr Wilson wrote to the Bar Standards Board requesting an investigation into the impact of the barristers' private relations on the role both played during the inquiry.
Lord Justice Leveson said it was "a matter for the Board to decide, what, if any, action to take", adding: "In the circumstances, I do not comment further."
But he unequivocally defended the role of Ms Patry Hoskins, who he said had "absolutely no input into any conclusions" reached by the inquiry.
More top news
Defending champions Arsenal squeezed into the FA Cup final despite a spirited fightback from Reading, who forced extra-time
A detective who led investigations into the Valley Parade fire tells ITV News there is "unequivocal" evidence the disaster was an accident.
Tonight will start off clear in many areas, but cloud will increase from the east overnight, bringing some light and patchy rain.