Two companies have already cut ties.
A representative for Paddy Irish Whiskey has said they will passing on a customer's concern over the signing of Paddy Jackson to London Irish "as a matter of urgency."
In a statement made on Facebook, the Irish whiskey company also noted that it would be "reviewing its partnership with London Irish in the coming weeks."
The response was prompted after a Facebook user asked them for comment on the signing through their public page.
The statement follows a week in which two sponsors cut ties with London Irish.
Cash Converters first issued a statement which read: "As a company, we are committed to the highest possible standards when it comes to our investments in any sponsorships and collaborations. As a result of a detailed and thorough review of our support for London Irish, we have decided to discontinue our association with the club."
Then on Thursday Diageo, who had sponsored London Irish for 27 years, discontinued their sponsorship following a meeting with the club. The company, which owns the iconic Guinness brand, issued a statement saying: "We have met with the club to express our concerns. Their recent decision is not consistent with our values and so we have ended our sponsorship."
Jackson was acquitted of rape following a trial in Belfast last year.
In April last year, Jackson's contract was revoked by Ulster and the IRFU.
At the time, Jackson said:
"I am deeply disappointed about the outcome of the IRFU and Ulster Rugby's internal review.
"However, I recognise that my behaviour has fallen far short of the values expected of me as an international player, a role model for the game of rugby and as a son and a brother.
"I am truly sorry."
