They above photos look quite familiar!
Living as I do in the USA, I never know which products are for sale in the UK. For example- “Loctite” is a brand that makes several chemical adhesives- one of which is “Red”. It is a liquid, that when applied to a nut and bolt will prevent the two from loosening, until heat is applied. It works very well.
I was able to push the rods back into both plungers, probably less than 1/4 inch, applying the red loctite first. Then I placed a center punch over the plunger and rod, and smacked it with a hammer, crushing the plunger just enough to grip the rod.There was enough adjustment available in the mechanism to let things still work, ie, catch and release.If Loctite, or something similar , is available- this may work! My repair is two years old, and I DO remove the tops sometimes!
Another way to tackle things would be to run a thread on the rod, and make an insert that would locate in the plunger with an internal thread to match! (If all else fails!)