I'm in my sixth week of my new job. I haven't had or signed a contract yet. I am hoping to leave and get a new job as this one isn't right for me. I assume the 3 month probation works both ways to see if I like the role and if they like me etc.. as I haven't signed or been given a contract as yet would I have to give notice and if so would it be a week?
There doesn't have to be a signed contract. Your notice period during probation may be set out in your offer letter or accompanying documentation. If that doesn't say anything about your notice period during probation you have to give one week's notice.