Absolutely. My family is very fortunate in having private healthcare (not that having it will help if needing emergency care).
However, I don't want a society where those who can't afford private get substandard care. I want a well-funded, and well-managed NHS for everyone in the UK.
I also want a move to holistic and preventative care - where all patients regardless of income or wealth or where in the country they live, have access to timely and effective help.
By preventative, I don't mean blaming the patient for "lifestyle issues" out of their control, eg. poverty harms health (which is why holistic healthcare needs to be provided together with addressing other societal issues).
So, timely access to effective and well-funded public services including but not only healthcare, and a supportive benefits system, better and more affordable housing, and job and education opportunities.
It's all related - and failing to address NHS problems and also the other issues is a false economy. More people in poorer health and then needing more help (healthcare or other help) than they would've needed if they'd had earlier and/or better help in the first place.
As an example of NHS false economy. The 5-10 min GP appointments, often with a different GP every time. Also the "only discuss one issue per appointment" rule (which ignores that often what might appear to be unrelated or irrelevant issues actually are related and relevant).
So, no time to get properly accessed and no continuity of care. Meaning things are missed or the patient is fobbed off - and ends up more seriously unwell, often longer-term.