Do you have any Humber bicycles. I have two in my collection along with two Super snipes series 3. One three speed manual with overdrive and the other auto. I live in New Zealand and have always been fascinated by old automotive history. New Zealand is very similar to England in many ways.
Funnily enough, my love of Humber cars never transferred to the bikes, mostly because of the front fork design. My favourite bikes are Raleigh and Rudge. Maybe I will visit NZ one day.
The pedal with the missing cap, looks like two odd Czech made ones I have (one of which is missing it's rubbers (removed to go on another pedal) & the other is missing a cap. The cap has a crossed through Z engraved on it. The inside diameter of the cap is 22mm. If that will fit yours then let me know & I will happily donate for free.