Can I give no notice if I don't have a contract?

[JesusDontWantMeForASunbeam]

For various reasons (I have another thread) I really can't return to my job. I don't have a contract (mat leave cover) but I have anxiety and the thought of working a weeks notice is making me really panic.

My plan is to go in tomorrow with my letter stating that I'm resigning with immediate effect but I'm a bit worried I'll get sued!

If you have an offer letter or they have given you particulars of employment, that is your contract. If the offer letter or particulars of employment says anything about your notice period that is what applies.

If you genuinely have no contract or it says nothing about notice you must give one week's notice as you have been there for more than one month. If you fail to do so they could, in theory, sue you for any loss they incur as a result. It is, however, unlikely they would actually sue you as any losses are likely to be small.

If you have anxiety and genuinely can't face going in you could sign yourself off sick.

Someone will correct me if I'm wrong, but in the absence of a stated length of time in a contract, employment law states notice period is a week. If you are unfit for work, you can self-certify for up to seven days off sick.