I’m not a doc but my wife is am ortho surgeon and she would never do an internet diagnosis, nor would any doc worth their salt.
Is the private hospital in Barrow (assume you mean Barrow in Furness) or in Manchester? If its in Barrow, it will probably be the same consultant and to be frank if it needs surgery the NHs will be just as good and theoretically as quick.
Mrs FD is of the opinion though that the better surgeons tend to be (not always) at the tertiary hospitals, which I assume is Manchester but I could be wrong. As they tend to be doing more routinely complicated and pioneering work. So the private surgeon in manc is possibly going to be more skilled and up to date but to be fair there want be much in it at all.
Private is usually good when you want to jump NHs Que, but in this instance if she needs surgery the NHS will be just as quick. Also private is great for quick in and out. After care tends not to be that great ie if complications occur, and if you have complications mid opp, private hospitals do not have life support facilities of NHS hospitals and you can end up being transferred in an ambulance to an NHS hospital. Having said that Private hospitals are nice hospitals with nice food and sky TV. Depends what experience your after.
Discuss it with the consultant. Mrs FD never minds people asking as long as they don’t go.down the route of the NHS is crap..