I currently have a 2 month notice period so given the current agreed upon start date with my new employer I'd have to give my notice in tomorrow. However, I am yet to have received a written contract with all the terms of employment (just an email stating salary, nothing on holidays etc) so I do not feel comfortable quitting my current job without all the details in writing. I have asked a few times for the contract and I was told I would receive it at the end of last week but didn't and since then I have not had a response to my follow-up email.
If I don't hand in my notice now this will mess up the agreed upon start date. Is it really such a bad idea to hand in notice without a contract or should I wait?
Edit: I should add this is in the UK to clarify due to differing employment laws