Meredith Alexander, who is one of 12 commissioners of the Commission for a Sustainable London 2012 watchdog, resigned from her post, citing concerns about Dow's relationship with the company responsible for the 1984 gas disaster.
After Alexander's resignation, senior Labour party figures such as Keith Vaz and Tessa Jowell (shadow Olympics minister) have also called for an audit of the process by which Dow Chemical was awarded the sponsorship.
However, London 2012 chief executive, Paul Deighton, insisted that after Alexander's resignation, it would not reconsider the decision to award the contract to Dow, which also has a 100 million pounds deal with the International Olympic Committee.
He said: "It is absolutely her right to make her point about how she feels about the victims of Bhopal. We fully respect her. She is one of 12 people who signed off on our process for choosing Dow to provide the wrap ?" so we carry on."
He added: "It is absolutely her right to resign. She is one of 12 members of that sustainability commission who signed off on the way we approached awarding the wrap to Dow. I think that it is great that we have got this independent function to oversee so all this is washed through transparently. I think that is fine but we are moving on."
The London Organising Committee for the Olympic and Paralympic Games (LOCOG) has consistently defended the process by which Dow was awarded the sponsorship contract.
Keith Vaz said: "Meredith Alexander's resignation was brave and principled. It is completely unacceptable that a supposedly sustainable Olympic Games is taking sponsorship from a company with as appalling a human rights and environmental record as Dow's".
He added: "I hope LOCOG and the Commission for a Sustainable London 2012 will now see that it is untenable for Dow's sponsorship to continue. The fact Ms Alexander felt it necessary to resign has brought the Commission’s credibility into question. It will remain so as long as Dow remains a sponsor of London 2012."
Jowell said: "I have called today for an audit of the steps taken that led the Commission for a Sustainable London 2012 to recommend to LOCOG that Dow Chemicals' sponsorship of the wrap was consistent with the high sustainability aims that we set for 2012".
She added: "We also need to understand what the role of other Commissioners was in the process which reached that conclusion. We need a solution not a row. Dow Chemicals need to understand the seriousness with which people take the continuing situation in Bhopal following the tragic disaster in 1984. I will do everything I can to make sure this issue does not overshadow the Games. There is still time for a solution to be found."