Football Association officials are to be questioned next month on their handling of anti-discrimination cases – including that of the former Chelsea doctor Eva Carneiro.

Members of the FA’s Inclusion Advisory Board say they have “deep concerns” about a number of cases and will question the chief executive, Martin Glenn, and the director of governance, Darren Bailey, about the issues raised at a meeting in November.

Top of the list of concerns will be the FA investigation into the independent board’s Heather Rabbatts, the chair of the IAB, which was launched after a complaint from two FA councillors about her criticism of the FA’s handling of the Carneiro case.

Carneiro parted company with Chelsea after being dropped from first-team duties following criticism from José Mourinho for going on to the pitch at the referee’s request to treat Eden Hazard on the season’s opening day.

Independent IAB members, including the former Chelsea players Graeme Le Saux and Paul Elliott, have written a joint letter to the FA chairman Greg Dyke and all FA councillors backing Rabbatts and criticising the investigation.

The letter, a copy of which has been seen by Press Association Sport, states: “The FA Inclusion Advisory Board members have expressed deep concerns about a number of recent anti-discrimination cases.

“To this end, we are looking forward to meeting with Martin Glenn and Darren Bailey to discuss these issues in more depth and in the hope that we can continue to support the FA and its values to see inclusion and diversity developed across the game. In the meantime, we wish to express our unwavering support for Heather Rabbatts and further, to seek reassurance that she still has the full support of the FA board.

“We were concerned to see two members of the FA Council question Heather’s integrity this week with an FA enquiry now under way. Their seeming priorities surely serve only to distract from the real issues at stake within football such as fairness, equality and respect.”

The letter says Rabbatts’ mandate is to champion equality and diversity in football. It adds: “We would question whether Heather Rabbatts has any charge to answer to and therefore, the IAB calls for this matter be concluded promptly so that she can continue unhindered in her many good works at the FA IAB helm and as a member of the FA board.”

Rabbatts has been heavily critical of the FA’s handling of Carneiro’s case and expressed “major concerns” about the disciplinary process, which saw Mourinho cleared of making discriminatory comments towards the doctor, after it emerged she had not been interviewed by the FA. She also questioned why no charges had been brought against any club after Carneiro suffered sexist abuse from opposing fans.

It is understood two FA members of the 121-strong FA council – the 82-year-old life vice-president Ron Barston and 70-year-old law lecturer Richard Tur, the chairman of the Oxford University FA – sparked the investigation into Rabbatts.

Under FA rules, only two members of the council are required for a formal investigation to be launched. The ultimate sanction if any wrongdoing is found would be Rabbatts being removed from the FA board, though any such move would have to be confirmed by her fellow directors.