That said, I would like to run a little consultancy on the side for people doing what I used to do. I have some potential clients lined up and finding work won't be an issue.
So from a legal point of view, do I register as self employed on the side? How will this affect my tax status? Can I join that Panama Papers movement?
How this works depends in part on where you're just acting as a sole trader (if it is just a small amount of additional income then it's likely just a case of declaring on a self assessment form and sorting out the additional NI) or whether you're setting up a ltd company (in which case get an accountant).
https://www.crunch.co.uk/knowledge/tax/freelancing-side-tax-implications/
What do you mean by "consultancy on the side for people doing what I used to do" btw... do you mean you'd be a "recruitment consultant" of sorts taking a fee for putting people into roles or indeed setting up an agency and getting a cut of the daily rate?
Check your employment contract carefully, this sort of thing might be prohibited or have restrictions especially if you end up working with/for similar businesses to the one you already work for. I guess if you're in a ancillary/support role and not really a part of the core business of your employer then it technically shouldn't be a big deal but you might well have a standard employment contract that has certain restrictions anyway. Are their potential conflicts of interest - like do you recruit people as a hiring manager in your work and might you also be recruiting similar people for this side project/external clients etc... another obvious one here is do you contract external agencies when recruiting - massive potential conflict of interest if you were to use some budget you have control over to pay your own side business/company for such a service.
Another clause to look out for is re: ltd company directorships, your current employment contract might need you to declare to your employer any directorships or ownerships above a certain % in other companies. Just in case you were hoping to keep this on the down low you might find, if you set up a ltd company, you're actually obliged to let them know about it.
In general most places don't have an issue with side businesses, the main issue is where it potentially overlaps with the employer's business. Even then if you're not directly competing with them or moonlighting for clients etc.. then it might just be the case that say they exercise (or attempt to exercise) certain rights over potential IP you come up with (probs not applicable in this case).