Both the UK and the EU have separate open sky agreements with the US. But that wouldn't allow a UK carrier to operate say CDG to JFK, or an EU carrier to operate LGW to JFK. It could't even be done as a fifth freedom service, since that isn't allowed between the EU and UK since Brexit.
If an A340 is mandatory (and why would it be?) then it would have to be a UK operator that has one. However, dispensations are possible in very specific circumstances, although these would be unlikely to be long term.