Is an offer letter sufficient enough to hand in my notice?

Sanne

2nd job - I only handed my notice in after references were confirmed
3th/4th/5th job - I handed my notice in on the basis of an offer letter (subject to refs) and a copy of the contract.

For job 3 I could have waited ages - turned out they never bothered with references.

As people have mentioned before, there is no such thing as security after handing in your notice (I'd even say until 2 years into a job and even then it's limited) beyond your agreed notice period.

Unless you have doubts about your references I'd go for it but ask for a copy of the contract and possibly the employee handbook.