You'll need to tell HMRC, for tax/NI purposes, this can be done online, but you can also call them. The second link specifically mentions your situation
https://www.gov.uk/working-for-yourself/overview
https://www.gov.uk/working-for-yourself/what-counts-as-self-employed
The forms are online and not too bad, though it will mean that you will have to do self assessment online at end of tax year. Though this isn't too bad, as you will know your PAYE numbers and presumably have a record of your self employed work (it's just putting numbers in boxes).
This web site has a calculator for your situation (I am sure there are others, this was first one on Google) -
http://www.employedandselfemployed.co.uk
The other thing to think about is, if you are invoicing them, do you need to charge VAT? You do not need to if you are not VAT registered and you are under the threshold, currently £83,000. This link gives HMRC detail on self employment
https://www.gov.uk/topic/business-tax/self-employed.
Hopefully you can determine whether it is worth your while.