The pressure on Richard Scudamore which began with sexist emails being made public, has increased after the Premier League's main sponsor registered "deep disappointment" and a member of the Football Association's inclusion board said Scudamore's position as chief executive had become untenable.

With the approach of Monday's meeting of a Premier League committee that will consider the matter, it has also emerged that the lawyer who is said to have referred to women as "gash" in the email exchange is under investigation by the City law firm that employs him. If Nick West is sanctioned, it would heighten the pressure on Scudamore and the Premier League.

Barclays, which pays £40m a year to sponsor the league, is understood to have conveyed its dismay at the contents of Scudamore's emails. In the original exchange he warns West in a conversation about a game of golf to keep a female colleague they nicknamed Edna "off your shaft" and trades sexist jokes.

Edward Lord, the inclusion advisory board (IAB) member who ramped up the pressure on the Premier League and the FA to act when he wrote to both to demand action, has concluded that Scudamore's position is untenable after the contents of the chief executive's email to club chairmen last Saturday night also became public.

In his note Scudamore stated that the looming revelations "had been obviously timed for our last day for it to cause maximum embarrassment to me and therefore the Premier League. The newspaper is asserting that some of the content is sexist and inappropriate. You will be the judge."

But Lord said that Scudamore's plea to the clubs showed the chief executive's later apology was insincere. "This seeming refusal to accept that the contents of his emails were in fact sexist and inappropriate to my mind completely undermines his public apology and leads to only one conclusion: that it was insincere and therefore unsustainable in the court of public opinion," he said.

"If it is that Richard Scudamore didn't believe that what he had written was wrong less than a week ago, I think it is highly unlikely that he has come to that conclusion in any reality since. On that basis it appears to me that his position is now looking untenable."

However, Scudamore would point to how his original email to clubs concluded: "These were private emails with no business context but, whatever the circumstances and no matter how these emails have come to light, I apologise and will ensure there is no such exchange in the future."

West, a sports lawyer who has been involved in advising the Premier League on broadcast rights deals and enforcing its copyright for several years, is at risk of disciplinary proceedings from DLA Piper. It is understood the investigation will be relatively swift. A spokesperson for DLA Piper said: "We uphold the highest professional standards as a firm and this matter is being fully investigated."

Meanwhile Women In Football has written to all 20 Premier League clubs and the body's acting chairman, Peter McCormick. In the letter, seen by the Guardian, it says "women in the football industry feel strongly that an apology is not enough".

It said it had been contacted by women across football who were "shocked and dismayed" by the content of the emails and the reaction from the football authorities. The letter is endorsed by Kick It Out, the equality campaign that celebrates its 20th anniversary next week with a dinner that Scudamore was expected to attend.

The England and Everton Ladies goalkeeper Rachel Brown-Finnis has told the BBC that Scudamore's emails were an "insult to all women" and said she would like to see him sanctioned. "However jokey he was trying to be with that, it's just totally unacceptable in this day and age," she said. "It's zero defence for me. Private emails when are you head of the Premier League don't really exist."

The Premier League on Monday said that Scudamore had immediately informed the 20 clubs, McCormick and Bruce Buck, the Chelsea chairman who heads the audit and remuneration committee that will meet on Monday, in line with its policy.

Lord's IAB, chaired by the FA nonexecutive director, Heather Rabbatts, will meet on Tuesday to consider its response.

When the FA said on Monday that it was unable to charge Scudamore with bringing the game into disrepute because it was a private matter, it sparked a backlash from staff within the organisation because it had failed to condemn publicly the sexist content.

Following intense criticism from politicians, and equality groups, senior figures from the FA, including Greg Dyke, the governing body's chairman, and its general secretary, Alex Horne, made it clear that they also disapproved.

The sports and equalities minister, Helen Grant, has criticised the contents of the emails and the shadow sports minister, Clive Efford, has criticised the Premier League's response.