Here she is, in all her glory, now named Cynthia. I looked her up on the Singer website, and apparently she is a 66K model, made at Kilbowie, Clydebank, Scotland on November 15th 1930, and somewhere, she has 999,999 brothers and sisters!
She's not flashy, but for an old lady, she's a little gem. I was lucky enough to download a free manual for a 99K (similar model) from the Singer site, whcih has given me a few clues on how she works. I'm off to get some machine oil and give her a little beauty treatment!