Mr Robinson claimed that he had only been made aware of the allegations on his return from holiday in Barbados on Monday.
Sources have said his shock resignation came after claims that he used gardeners employed by Woolwich to carry out work on the grounds of his home in the village of Brasted, in Kent.
Mr Robinson, 54, was also alleged to have borrowed a company Range Rover for use by his family, in addition to having decorating work carried out on his pounds 450,000, six-bedroomed mock-Tudor house.
But in a statement issued through his lawyers, Mr Robinson, who was ousted after a board meeting, said he was "totally shocked" at the action taken by the society.
He said: "The first I heard from the board was on Monday afternoon. This was after 33 years of unblemished service with the Woolwich, of which I am very proud, and culminating in my appointment as chief executive only three months ago.
"I deny that I have in any way misused the society's facilities and the matter is now in the hands of my solicitors."
Henry Clinton-Davis, a partner at the law firm DJ Freeman that is representing Mr Robinson, said the matter was being examined to decide on what course of action to take.
A Woolwich spokesman said: "Mr Robinson is entitled to his views but our action was based on an irreparable loss of confidence on the part of the board and management."
It is believed that unless a settlement is reached, Mr Robinson's resignation might preclude him from compensation for the sudden end of his rolling two-year contract, paying pounds 300,000 a year. However, at the formal retirement age of 62 he may still be entitled to pension rights based on his 32 years of service with Woolwich.
The society's chairman, Sir Brian Jenkins, said: "The allegations centre on the irregular use of the society's facilities but there are a number of matters under investigation."
It is understood that details of the alleged irregularities surfaced very recently after an internal audit. Non-executive board members, including Sir Brian, met on Sunday to discuss their findings.
Mr Robinson is thought to have been summoned to a second meeting at the home of Sir Brian in Blackheath, South-east London, on Monday afternoon. Among others at the meeting was Lord Borrie, another board member.
The following day, at a meeting held at the society's offices, board members discussed the results of the audit. Two hours after a break for lunch, Mr Robinson resigned.
His departure comes just a year before the society, the UK's third-biggest, is to seek a pounds 3bn stock market listing.
A spokeswoman said the plans for flotation to a bank "remained on track". More than 3.5 million members will receive a share hand-out worth an average of pounds 800 each if the society succeeds in its plan.
Mr Robinson, who started with the society as a management trainee, was seen as the driving force behind the flotation plans. There had been speculation that he has not had an easy relationship with Sir Brian, a former Lord Mayor of London and City accountant. This is being officially denied.
Former chief executive Donald Kirkham is taking over as head of the society until a replacement is found.
Among those strongly tipped to succeed him is Woolwich operations director John Stewart, who as Mr Robinson's right-hand man, has the task of finding suitable acquisition targets for the society.
Mr Kirkham, chief executive for 10 years before Mr Robinson's appointment, was once a strong opponent of conversion.
However, a Woolwich spokeswoman reported Mr Kirkham as saying yesterday: "I may have been described as a high priest of mutuality, but I have now changed religion." The society also claimed that the decision to float had been reached unanimously by its board after a two-year review at Woolwich.
Rob Thomas, a building society analyst at UBS, argued that the flotation was still likely to proceed as planned.
Comment, page 23Reuse content