There is more than one reason to give economic aid to a particular area. This answer will focus on the Pitcairn Islands but it's applicable to every other example you've used.
The Pitcairn Islands are a British Overseas Territory, which as the CIA world fact-book rather succinctly puts it means that it is one of the last vestiges of the British empire in the pacific. Now the population of the Pitcairn Islands is only about 50 people, so as you rightly put it they have a negligible direct voter impact, but what they do have is indirect voter impact. Most people in Britain are proud of the empire, this may seem silly to someone thinking from an extremely logical point of view, but abandoning the Pitcairn Islands would be similar to saying that Britain is no longer a country able to support it's empire, thus with a mixture of Pride and Fear the government has supported and will continue to support the existence of life on the island, as British voters support the existence of the empire.
Another point is strategic, imagine for a moment that Britain hypothetically declare war on Australia. Now imagine instead of British soldiers after bombing Australia, they develop some engine troubles and are unable to fly the 16,000 odd kilometers back to Britain they can fly the much shorter route and rest in a British Island which has access to water, electricity and the internet. Although there may be no military base there right now, spending millions of pounds to build such infrastructure means it will be easier to commission such a base in future if need be.
My last point is economic, one point that literally everyone overlooks is that is Britain owns the Island it also owns the water around the Island, and all the resources under the water. Here is a map that shows the global distribution of territorial waters. So if 10 years down the line the worlds biggest crude oil deposits are discovered in the pacific, Britain has according to the UN law of the sea, a lot of claim on the natural resources. This is also one of the reasons why Britain so voraciously defends it's claim on the Falkland Islands. So no the island doesn't have negligible economic significance.
Also who would go to a national park on an uninhabited island in the pacific? Even hosting a park requires some population who will then need basic resources likes schools, clinics, ferry's etc. which is exactly what Britain is paying for.
