Contract ending and concerned about maternity pay

I am employed on a three-year fixed-term contract that will end in October when the project I am working on comes to an end. I am pregnant with a due date around mid-January 2018. As I will still be employed by the company by the 15th week before EWC, and will have been employed on a continuous basis for more than 26 weeks by then, I believe I am entitled to SMP. Is it possible to start maternity leave after the expiry date of my contract. Also my employer provides enhanced maternity pay for staff who have worked continuously for 26 weeks by the qualifying week and who intend to return to work for at least 12 weeks after maternity leave.  Does this mean I could ask for enhanced maternity pay, even if my maternity leave would start after the expiry date of my current contract, and not be expected to pay it back or, does this mean that, as my maternity leave would start after my contract expires, so when I am no longer an employee, I do not qualify for enhanced maternity pay?