A cheque being merely non-negotiable would not stop you cashing it. It only means the cheque cannot be presented by anyone other than the payee. However, it's also likely to be "crossed" and marked "A/c Payee" or "A/c Payee Only". Most cheque books are now printed this way. A crossed cheque can only be paid into a bank account and cannot be cashed over the counter. If the cheque is crossed AND marked non-negotiable it cannot be cashed would have to be paid into an bank account in your name. It would be worthless to anyone else so prevents someone else cashing the cheque for you - i.e. Giving you the cash and putting in their own bank account .
Negotiable are accurate
With the non-negotiable you cannot pay it into any account unless the one written on the cheque, but with the negotiable you can give it to another person to pay it into an account