His decision to pick up the gauntlet when his local hospital was closed four years ago was fuelled, he says, by a deeply felt belief in the NHS as a basic right for all taxpayers, rich or poor.
"My mother was a nurse. I've got a lot of time for nurses and doctors because of what I saw her go through. The NHS is something our tax money buys. It's like education. That was the deal, I always thought. We're finding now that it isn't quite the deal and there has to be massive private sector funding."
He is outraged, but has resisted calls to use his superstar status in a national campaign against health cuts. "The way to get involved in national campaigns is to get involved locally. When we went out on tour a couple of years ago we had a slogan which was to do with the environment, but it might as well have been to do with health. It was, 'Think globally, act locally'. It was a Friends of the Earth slogan, actually. I nicked it. You do your bit."
His "bit" has involved leading a four-year campaign to save Rye Memorial Hospital, which will reopen later in the year as a care centre jointly funded by local health authorities and social services. He got involved when a teenage asthma sufferer whose attacks had previously been treated in Rye died on his way to the nearest casualty department, half an hour away in Hastings.
"From that point on everyone closed ranks and it was like, 'We're gonna do it come hell or high water,' " said Mr McCartney, who put nearly pounds 1m into the campaign. He has a world record of 87 gold discs and is reported to be worth pounds 420m, but still described his donation as "a lot of money". "It was more than local people could normally have afforded. I'm loth to go shouting about the actual amount. Then we had to raise more on top of that."
Paul and Linda McCartney had offered to pay nurses' salaries to keep the old hospital open, but ended up funding a campaign worker who put the idea for the new, collaborative centre together. But in victory this weekend there is also a certain amount of sadness. "It was OK for the local people here, they've got a celebrity like me who can give that little bit of extra money and can help with the publicity," he said. "I feel sorry for the people who haven't, who are just subject to the rules. Of course, their hospitals are still closed because they can't afford to do what we did."
Neither do they have the media hanging on their every word. "If we had a demo with me leading it, it was likely to get into one or two papers. Otherwise it barely makes the local news. That is what saddens me. The people who haven't got the local celebrity and the pulling power must have to work 50 times as hard."
He described himself as "ringleader" to a campaign that was fought hardest by other locals, using the traditional weapons of coffee mornings, jumble sales and sponsored events. "We're amazed that we won. I put it all down to people power, because there was a hell of a lot of local effort and massive campaigning, visits to Westminster and stuff."
But why didn't he just provide the pounds 5m it required to resurrect the hospital? "The thing about the dilemma behind the headline 'Local Celebrity Aids Cause' is that you can do too much. You can make all the local people think, 'Oh look, he's just on an ego trip, he's just trying to buy us a hospital.' I like people to be able to say, 'I put a fiver into that.'"
The man who sang "Money can't buy me love" is famously proud of his working- class roots, but has also been criticised as mean. "People say, 'Oh no, you're too rich to be working class' and I say, 'No, no, it's a state of mind working class, it's not a bank balance.'
"At our kids' local little school, for instance, they're collecting for a computer. Obviously, I could just buy them 10. But then it's a different ball game. What we would do is say, 'Raise a lot of the money yourselves and then we'll top it up.'
"We'd make sure we didn't give more than half what was required. It's a double-edged sword doing anything. You could also just bury your head in the sand and say, 'It's nothing to do with me.' Because in actual fact, I'm all right, Jack. It's not really my problem."
Indeed not. The McCartney family subscribes to a private healthcare firm. "For a long time I was NHS. My kids went to state school. I pay taxes, I pay more than most people, therefore, I'm entitled to what taxes are supposed to reward.
"However, at a certain point I thought it's all very well sticking to the rules but there is the perception ... people say, 'Rich bastard, why is he going on the NHS?' It's no good for me to say, 'I pay taxes, I'm just like you.' So we decided we'd better go private, just for the sheer perception of it."
His youngest son James, a 17-year-old student, was the subject of a coastguard search when he went missing while surfing in 1993, and was airlifted to hospital in Hastings in May this year when a Land-Rover he was driving on the family estate overturned and pinned him down.
"After the sea rescue some people said, 'Oh, why's his bloody son got the helicopter?' I say, 'What do you mean? My son's entitled just like your f***ing son.' What do they want to do, leave him because he's rich? Would they say, 'Hang on, check his Barclaycard. Oh no, he's flush. Leave the bastard to drown?' It's not on."
On the other hand, the McCartneys are grateful for the protective attitude of those who live around their estate near Peasmarsh. "You get tourists coming around here who will ask, 'Where does Paul McCartney live, please?' And they say, 'Who? Never heard of him, mate.' They give it the country yokel bit."
He describes himself as "very much a local person". "I'm asked to open bazaars and things, but generally I say no. The kids around here all think of me as my kids' father. Which is great. I like that. It's a good balance to what I am on tour."
In November, ITV will broadcast The Beatles Anthology, a series put together by the surviving members in which will they will perform two previously unfinished John Lennon songs. These will be released on an album of rediscovered recordings, through which Paul McCartney and the Beatles' producer George Martin are currently sorting.
"It's deja vu, actually," he said. "We're sitting in Abbey Road studio number two, where we always worked, listening to the work that we did when we were 20. It is quite strange, but quite exciting as well. It's like being archaeologists.
"We're actually finding tracks that we didn't remember recording, that we didn't want, or thought, 'No, that's not too good.' Now of course, after 30 years, they don't look too bad at all."
But if the material wasn't considered good enough then, why release it now? "I do believe there will be a bunch of people interested in hearing the George Harrison song from 30 years ago that no one to this day has ever heard. It's not the greatest thing George Harrison ever wrote, but it's an undiscovered nugget. If you find a little Egyptian pot, it doesn't have to be the greatest Egyptian pot. The fact that it's Egyptian is enough."