Hi, as a Brit and mentor, but not a teacher, I would explain as follows:
"The union executive clearly can’t deliver its membership" means that no matter what decision(s) the executive make, they cannot guarantee that the individual members of the union will abide by that decision.
If the executive negotiated a deal with the company's management, to end the strike, many union members would ignore the deal and remain on strike to try for a better deal.
Hope this helps.
- For Teachers