Martin Glenn, the Football Association’s heavily criticised chief executive, faces further embarrassment after admitting the organisation deliberately chose a black woman to investigate the Mark Sampson race allegations – without apparently realising the FA’s lawyers had already sent a letter to the Guardian warning such a claim was “plainly false”.

Glenn, one of the executives most under scrutiny after Sampson’s sudden sacking on Wednesday, promised he would offer a personal apology to Eni Aluko and Drew Spence if the controversial and reopened independent inquiry found that the now‑deposed England women’s manager had made racial comments to the two players.

However, Glenn also went on to say he had made it a condition to have a woman who is not white in charge of the inquiry, without appearing to realise that the FA’s solicitors, Farrer & Co, had written to the Guardian on 25 August to say that any suggestion that it had deliberately chosen a black woman would be inaccurate and construed as a personal attack. “That suggestion is plainly false and categorically rejected,” it read.

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In an even more strongly worded letter, the same legal firm followed that up on Thursday by saying that the colour of Katharine Newton’s skin had been “utterly irrelevant” in the selection process and only an issue for those who did not understand, or wished to undermine, the investigation.

Yet the FA’s inability to get its stories straight resurfaced when Glenn agreed to face the Guardian’s questions about the criticisms of the initial internal review – carried out by the FA’s technical director, Dan Ashworth, and the human resources director, Rachel Brace – in the face of criticism from the Professional Footballers’ Association that it was “not a genuine search for the truth” and “a sham which was not designed to establish the truth but intended to protect Mark Sampson”.

Glenn defended his colleagues but admitted he was still not fully satisfied at the end of the initial review and said he had brought in Newton – whom he referred to as “Kate” – because he had decided the second investigation could not be overseen by a white person.

“I wasn’t certain that two white people [Ashworth and Brace] – two middle-aged‑ish white people – doing the inquiry may have seen some of the shades of the issue that Eni was trying to get at. So, quite deliberately, I said: ‘I want an independent look at this and, to be blunt about it, I want it to be an employment expert, I want it to be female and I’d like it to be of a different ethnicity to us,’ in case we were missing things and in case the way we had done the inquiry may not have made people of a different ethnicity comfortable to speak up.”

That, according to Glenn, was “above and beyond what normally would have been done. I feel good about doing that. You can pick holes but I’m not going to get into a ‘he said, she said’ about why some things were raised. You can deal only with complaints that get raised, not total hearsay. It was a full investigation.”

Glenn and his top-level colleagues, in particular Ashworth and the chairman, Greg Clarke, are under scrutiny after Sampson’s dismissal and being forced to admit they had never fully looked into the safeguarding investigation surrounding a complaint about his behaviour and relationship with players at Bristol Academy, his previous job.

With the FA still under pressure to resolve the escalating story involving Aluko and Spence, Newton’s investigation has led to criticism from, among others, Kick It Out, the PFA and Women in Football. Glenn, however, appeared to indicate that Spence was at fault for not coming forward earlier. “If someone has had something said to them, the thing you would expect them to do is raise a complaint. The specifics of that complaint could then be dealt with. If you worked your whole life on hearsay, you’d never be able to run a classroom let alone the Football Association.”

Spence, then 22 and on her first England camp, chose not to make a complaint about an alleged incident at the China Cup in 2015 because she feared it would end her international career almost before it had begun.

Instead, it was Aluko who raised it with the authorities. Yet, over two inquiries, Spence was never asked to corroborate whether it was true that Sampson had upset her, a mixed-race player, by asking how many times she had been arrested. Newton did not interview any of the other players who were present but has agreed to meet Spence on Friday after the player submitted a statement backing Aluko’s version of events.

Aluko alleges separately that Sampson told her to be careful her Nigerian relatives did not bring Ebola to a game at Wembley. Sampson has always denied all the claims, and continues to do so, but Newton is now under considerable pressure to interview the three players – Jill Scott, Jo Potter and Izzy Christiansen – who were in the relevant meeting with Spence.

“It could very well be the case that Mark said some crass things,” Glenn said. “I don’t know, you won’t know and I suspect no one will know. If it’s true that he has made inappropriate comments to Eni Aluko and Drew Spence I will apologise. He doesn’t need to – but I will apologise on behalf of the FA because we don’t operate the ship like that.

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“But is there evidence of systematic racial bias, or bullying, in that national team? Absolutely not. Two inquiries have shown that. We’ll finish the work after she [Newton] has spoken to Drew. But it’s not one [a culture] of systematic bias. I have to apply the principles of natural justice to this.

“Of course people like Eni have rights that need to be respected. So, too, does the FA. So, too, does the management. So, too, do the support staff.”

When it was put to him again that there were obvious holes in the investigation process, Glenn said: “I disagree with you on just about every count. I’ve worked in big organisations where inquiries into this kind of thing have gone on. I’m very comfortable. We did the internal inquiry with the head of HR and Dan Ashworth, both of whom have got a value set I totally respect. In terms of the question ‘is there any evidence of systematic wrongdoing?’ clearly not.”

He added: “I respect your opinion, I just disagree on the substantive and I’m happy on the Eni Aluko issue. We’ll keep an open mind and my opinion will change as the facts change. I’ll see what the final conclusions of Kate’s inquiry are and, as things stand, I’m very happy to defend what we have done.”