Does email suffice in place of signed contract?

I quit my job only for the company to ask me to stay on for another few months after my official leave date.

I agreed to be hired as a freelance sole trader but after asking for a contract, they said that the email would suffice.

The email is not from HR but from the hiring manager and states the day rate, the number of days to be worked per week and the dates to and from I will work.

Is this ok as they say or do I need to produce a contract myself and ask for it to be signed?
If so, how do I find a contract template?

Thanks