Both ISBA and the IPA are concerned that Billett, who owns a commercial media auditing company, is sitting on the panel to select the person who will take on this key role, while their views have not been sought. The appointment of an adjudicator is a consequence of government approval of an ITV merger.
The matter is complicated by the fact that Bob Wootton, ISBA's director of media affairs, has been interviewed for the job of adjudicator.
Jim Marshall, the head of the IPA media futures group, said: "We are unhappy that advertisers and agencies are not more involved. I don't know why John Billett was asked - I suppose they were looking for a degree of technical expertise."
Bernard Balderston, the associate director for media at Procter & Gamble, said: "I can understand the reaction of ISBA and the IPA because an adjudicator is in place to protect the interests of advertisers ... the only other concern relating to John Billett is that in some of his submissions he made some reference to his organisation undertaking part of the adjudicator role."
The part-time job attracts a salary of up to £100,000 and there is intense competition for it from people who have recently left the industry.
Among the frontrunners are David Cuff, the former vice-president of commercial at Flextech Television and David Connolly, the former Starcom Motive chairman.
Interviews are currently being held and an appointment is expected at the end of this month.