On the other hand, I can see the other more powerful Security Council countries leaving and setting up something else (to which the UK, now a rather middling power, will not be invited).

6th largest country by GDP out of 195 is a strange definition of "middling".

India is 5th largest GDP and also a nuclear power, it is not a permanent member and does not have veto power on the SC. Germany/Japan are higher than both India and U.K. and still not part of council for obvious historical reasons. GDP and nuclear arsenal are just two aspects to power, lot more to it than just that.

When France and UK became part initial members the SC. They were still colonial powers controlling a lot of the world, and won the war, they are no longer have that kind of strength or influence.

If a new council were created in the somewhat near future it would be because power dynamics have shifted far enough that the current council is no longer useful, from the current members UK and France are most likely to ones for that shift and not enjoy similar rights. New powers at the table could be EU as a whole, India, Brazil perhaps Japan and Germany etc.

As it's the security council, I think a functioning military would also be a requirement. Germany and Japan don't have this.

Germany and Japan have functioning militaries; they have legal restrictions on their use, but those restrictions don't, IIRC, obstruct their participation in anything that the Security Council would decide.