As Anais says, it’s down to Trust policy. However it maybe that the Trust policies need revisiting if they are overly restrictive. This is the NHS guidance Q&A for clinical staff which clearly states:
Clinical private practice
12. I carry out some private practice in addition to my NHS role. Is this ok?
a. NHS commitments should always take precedence over private work where there
might be a conflict of interest. Otherwise, private practice is fine as long as you
declare it to your organisation on appointment or whenever any new private
practice arises. You will also need the prior approval of your organisation, except
for in emergency situations, and you should not initiate discussions about your
private professional services with patients, or ask other staff to initiate such
discussions on your behalf. You should not accept direct or indirect financial
incentives from private providers other than those allowed by Competition and
Markets Authority guideline
The onus is on the clinician to declare the private practice and then the organisation decides whether this does in fact constitute a conflict of interest in their view.
In my experience, some Trusts prefer to go with a broader, blanket geographical rule (I guess because it’s clearer and less open to interpretation) when in fact it may not constitute an actual conflict of interest. I guess a clinician could try and contest this but in the end if that’s the Trust’s guidelines they can still refuse. I do feel that there is a pervading attitude in some Trusts where private practice is seen negatively and the constraints around this are overly harsh.