The British people have been consistently indifferent to the fate of the Navy since about 1970, maybe even earlier. We make our own bed and we will all have to lie in it.
Same is true for all our armed forces. Don't kid yourselves into thinking that people give a moments thought to the disposition of the RAF or Army either.
It's perfectly natural - all populations grow to under appreciate their armed forces during extended periods of peace at home. And WWII is now a dim and distant memory, and even today's young teenagers weren't born at the conclusion of Gulf War 2.
The RN has an important role to play. There's the ultimate Top Trumps winner - the nuclear deterrent. And whilst it's strike capability is small, it can put a Tomahawk down almost anywhere in the world at quite short notice and gives no prior warning of impending doom. In contrast the RAF often has to go and ask about borrowing an airfield somewhere before it can do anything, which limits it's usefulness when something discrete is called for.
And for a lot of the things going on at the moment, small discrete involvements are definitely flavour of the month. They always have been - the trouble in Malaysia and Borneo were successfully dealt with without the large scale involvement of RN, RAF and Army, back in the days when all three were much larger.
The thing that is generally quite tricky is "What to do About Russia if they Invade". It'll probably never need to come to it (all of Putin's money is in Switzerland; not even he's going to risk blowing his retirement plan...), but all of Western Europe would need to seriously tool up fast in all departments, not just the UK.