Mrs Bercow, an outspoken Labour supporter, was invited to attend the service as the wife of her husband, John, who will be going.
But in a statement today, she said that she was not obliged to accompany him in the performance of his public duties.
She also accused No 10 of leaking details of her decision not to go to the press in order to try to undermine her husband.
"As Commons Speaker, John will be attending the funeral - and rightly so. But I'm not obliged to participate in my husband's public life - last time I looked, this was the 21st century! John holds public office and an important position, not me," she said.
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The RMT union has accused Southern of inventing figures which the company claims show record numbers of guards are going sick.
Thursday morning's weather for the west of the region
Thursday morning's weather for the east of the region