Yep, I am pretty sure it means you have to take at least 6 weeks off after the birth of your baby. They wouldnt make you work right up until the day your baby is born. You just have to give them 4 weeks notice of the actual date you want to start your leave.

I remember when I was applying for my maternity leave, they told me I had to start my maternity leave 6 weeks before my babys due date, but if I got a medical certificate to say I was fit to work later than that then I could... so I did and I worked till 37 weeks. But either way, I had to have the first 6 weeks off after she was born.