That settlement offer had included commitments on working hours and annual pay rises in exchange for the cabin crew workers agreeing to BA's planned £62.5m of cost cuts.
But after announcing that the strike would go ahead, Mr Woodley said the airline "did not want to negotiate".
"I am extremely disappointed for the travelling public and our members, but this union will now support our members, while remaining open for talks with the company," he said.
"It is an absolute disgrace and an insult to our people that [Mr Walsh] tabled a deal that reduced the amount of pay on offer.
"It is ridiculous to expect anyone to go to their membership with a worse offer."
Mr Walsh said suggestions that he wanted to break the union were "absolute nonsense".
"We have spent 13 months in negotiations. BA has been at the table, ready, willing and able to negotiate. If people want a scapegoat, they will have to look somewhere else."
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