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This photo is from wikipedia and it says it is from 1962. The down tube seems to have a face. Could it be Jacques Anquetil? I know she did have one of his frames, not the same head badge shape as your photo, but it is an idea.
Yay, happy to get a reply! Yes, you are correct, Beryl is on an Anquetil bike. But this photo is from the 1967 Worlds pursuit in Amsterdam.
From photos I've seen, Beryl rode Mercians from 1959 through 1961, road and track, in various colors. She rode the "mystery" bike in 1962, at least on the track, in chrome. In 1963 and 1964 she rode Viking bikes on road and track, usually red with white head. From possibly 1965 through maybe 1971 she was on Anquetil bikes, road and track, at first they were blue, and later silver. From about 1972 to maybe 1980-ish, Beryl rode Ron Kitching bikes, various colors. From then on she appears to have ridden Raleighs, including an SBDU out of Ilkston. Possibly the last bike she rode had BERYL on the down tube, and looks like it was badged Raleigh.
On the cover of Beryl's autobiography "Personal Best" is a good shot of her on the 1962 mystery bike. Maybe the answer is inside the book? I've yet to read it. I'm still reading through Jeremy Wilson's 2022 "Beryl", and it's an absolutely awesome read. Highly recommend.
--Joe