Fingers like lightning
Get yourself some IR35 insurance that covers current and past contracts. If that’s possible.
It doesn’t seem like you have done your due diligence up till now.
Super poster
The percentage in private sector will probably be higher than in the public sector. There are probably more in the private sector that will be willing to take the risk of an outside determination, since it is generally going to save them money to do so. I'd guess they will also be willing to be more flexible, in general, in structuring contracts and working practices to be outside.
And they aren't likely to have some NHS guy telling them all to make blanket inside determinations.