Thank you all for your information on where to source those records.
Flatteric, yes it's Harriet and it seems maybe she stayed longer in the workhouse. William Hart Flute was born to her alone in Bedford in 1848 and she is shown as a 'lacemaker' in the census for the workhouse in 1851 so maybe she had no alternative but to take him with her, listed as 3 years old. She had a daughter born in 1853, according to the record, in Newport Pagnell. I have ordered their birth certificates in the hope they supply more information. My curiosity came from how long she could have been in that workhouse? Somehow she resolved her situation and came back to her family in Astwood Bury by 1861, then married a Thomas Fensom in 1862 and raised a second family. She lived close to all her Flute relatives and next door to her first son for the rest of her life. Some stories have happy endings.