Freelancing while employed part time

[MadMum2015]

Hi
I work in a small consultancy firm which is suffering a bit of a slow down so, as the most expensive employee I've been asked to go to 3 days a week.
Not ideal of course but better than redundancy. Realistically though I can't afford to live on 3/5 my current earnings. So my question is, can my employers legally refuse to allow me to top up my income by freelancing? The challenge I can see is that anyone interested in my skills is likely to be in a competitor firm so my employer may try to prevent this. It would certainly breach the terms of my full time contract, which is completely standard for our industry but equally is it a restriction of trade when they are changing my contract to part time?
Suspect this makes no difference but I've 4 years' service with this company.
Any thoughts / experiences much appreciated!

They can't stop you freelancing but obviously they are likely to be unhappy if you work for a competitor. Do you have a non-compete clause in your contract?

Would you actually be better off taking redundancy, then freelancing for current company AND picking up other clients? They can't restrict who you work for if you don't have a contract with them.