Yep, there's one of these that disintegrates in the same way situated in the middle of the hose that feeds into the heater control valve - at the top of the pic:-

Believe me, it weeps after 32 years or so...
The current replacement hose is the one below below and costed me about £70 by the time it dropped on my doormat

so I wish I'd known about these inserts at the time. I found I needed to replace the control valve at the same time since it fell apart in my hand, so I suppose the weep did me a favour - albeit an expensive one
Btw what size are they and what are they called? I'll be able to keep the hose 'on the shelf', now...
edit: I reckon a plastic connector (like that heater control valve) would be a longer-lasting method to join these pipes?