Royalist,
On the contrary, since Crimea and Ukraine I don't think that NATO has EVER been on more solid ground. If any politician is asking whether NATO serves any purpose then they have had their heads firmly buried in the sand for about a decade and a half.
A lot of NATO is not in the EU, I don't see what on earth difference it would make to our continuing NATO membership if there is a UK exit from the EU?
Oh, and "Such involvement should be in pursuit of our national interests and nothing else." Sounds SO like the 1930's appeasement rhetoric over Czechoslovakia.