You can potentially save tax/NIC by putting freelance income through a limited company: however, you are not permitted to pension such income through the NHS scheme.
Now that the practices are responsible for paying the 14.3% employers contribution – and are using that to negotiate fees downwards (unless you’re part of a locum chambers where you have much stronger negotiating power) so their net costs don’t change , some of that advantage may have been lost. However you should not underestimate the value of the NHS pension scheme.
Let’s assume a worst-case situation, where a practice will pay you the same amount whether you are in the pension scheme or not. As a self-employed locum earning £80k a year after expenses (before deducting superannuation), you’d be left with £44,128 in hand after superannuation/tax/NIC.