Well, as part of the new aircraft carrier-centred "big ship" naval upgrade, the JSF is one of Britain's key defense projects (the others being the FRES rapid deployment armored vehicles and the replacement of the strategic nuclear deterrent). All of these have a substantial American component, and for Britain to pull out of one for ITAR reasons, it has to raise questions regarding the other projects.
I think there is real tension between Britain's economic alignment with the European Union countries, vs. its military alignment with the UKUSA countries (US, Canada, Australia, New Zealand).
If the Americans unreasonably limit access to weapons systems, the UK will necessarily purchase them from its European allies. I'd suggest that this would have the outcome of strengthening European military capability, while diminishing American influence over British foreign and military policy.
Let's hope the US Congress comes to its senses
(edit:shortened)