I don't think so, because the JSM doesn't fit into the internal weapon bays of the F-35B. That means they can only be carried externally and as such interferes with the stealth characteristics of the plane.
The UK is focusing on Spear 3, which can be carried internally and in far larger quantities. We're also developing FC/ASW with the French - JSM would mean a third type of AShM for the Royal Navy to operate and maintain.
Therefore, in my view a JSM purchase would signal the belief that the Royal Navy was likely to tangle with a significant naval power like the PLAN within 12-24 months and immediately needed an AShM for its fighters. Russia doesn't pose the same threat.
They are all pretty much unique weapons in their own right.
Spear3 is 100kg missile with ~5-10kg warhead
NSM is a 400kg missile with ~100kg warhead
FC/ASW is a 800kg+ missile with ~200kg warhead and 2x50kg effectors.
This is similar to the idea that NSM and LRASM are very similar missiles doing exactly the same job, they are very different, and a unit might carry both, or different units might carry one instead of the other depending on mission.
Even though JSM doesn't fit into a F-35 weapons bay, it is still a very stealthy device if carried externally and fired at range. It would still be a lot smaller, lighter and is a here today weapon. However, there is no usefulness today JSM and F-35, as there is no integration, wait for blkIV. JSM is supposed to go into production in 2023.
Particularly as there is talk about a JSM variant that may be able to fit into F-35B bays. It may have a smaller warhead (25-50kg), but that would seem possible. It would be a very useful weapon. Hitting much harder than Spear3, but internal and much lighter than FCASW. ~!6kg of spear3 is pretty light. 300 or 500kg warheads are pretty heavy. Plenty of room for something in between.
I would expect RN to look at JSM after BLKIV is out and people know how well that munition works with that platform, and if there is any internal B version on the way. No reason to even really look at it until then. There is some overlap with existing and future weapons, so it would need to be assessed on the state of play at that time. Entirely possible the FCASW doesn't happen, or doesn't happen in time. But at the same time, there are other options as well, and other F-35B operators, looking at other combinations. I imagine it would be looked at post 2025.
