Blimey - thats the sort of uncommon thing that may turn into a lifelong quest !
Can you track down the originals ? Always a good line of enquiry.
Are you a member of a James Club /Forum.
A direct connection to other owners may turn up a spare set.
Probably cost you to be a member though.
Diligent searching on ebay, gumtree, car&classic etc may turn up a set.
https://www.ebay.co.uk/sch/131090/i.html?_from=R40&_nkw=james+cadetEvery time you see cadet parts advertised, ask if they have any plunger parts.
Don't be a pest in this though, use moderation !?
Surprising what this will turn up though.
That 'diligent' needs emphasizing though, it may take years, searching every few days.
Ask me how I know this.... But unicorns and hens teeth do turn up now and then.
Good Luck. !