I know we've all got very taxed on various fronts over this post!
I think what the OP is saying is that the NHS is a victim of its own sucess. When it was established, the idea was the it would work hand in glove with welfare reform, social care, etc. People would take responsibility for their own health, and only use health services when very ill. All paid for via NI.
However, after only 2 years, the Labour govt realised it was becoming too expensive, so reintroduced dental and presciption charges. In addition, initially people were v grateful and were more aware of how to prevent illness, and things like housing and sanitation improved. But as years have passed, people have taken less responsibility and think, oh, the nhs will fix me (gastric bands for example). Add to this the brilliant research, etc which has found cures for many diseases/injuries, and disaster ensues!.
People are living longer (yayy!)) but using more resources because they have become lazy about their health (not everyone, I hasten to add!). Over the years, NI contributions have dropped dramatically due to unemployment and Budget 'treats', the NHS has been constantly tweaked and now needs an army of managers and bean counters to ensure these behethmoths try to provide a basic service.
This has created a pefect storm, and a big fail.
So, the simple answer to OP is yes, living longer is affecting others, but being kept alivecat any age, where previously treatment wasn't an opition, is contributing to longevity.