Volunteer church flower arranger here - there are about a dozen of us on a rota, and we often give up our Friday afternoons & evenings to decorate the church for weddings, and we love to do it. What happens at ours is that either we suggest that the bride gives us a colour scheme and some money in advance so we can source the flowers, or that a florist delivers the flowers to us and then we do all the arranging. We will also provide oasis and loads of greenery to include in the arrangements - that way the flowers can go a very long way (!) and you don't need to spend anything like as much money.
Quite often, the bride will organise for a florist to do pew ends, or displays outside, and they will usually be taken away by the bridal party for the reception. Otherwise the flowers are left behind in the church.
Most of us have been doing flower arranging and church flowers for decades, and yes, we do know what we are doing. We also know what works in the church and what doesn't, and the quantities needed.
To give you an idea - we could do a massive pedestal display with less than 20 quids-worth of flowers. A florist would probably charge hundreds for one the same size.
September wedding eh? You might find that the wedding day is right in the middle of the Harvest Festival period, when the church will be bedecked all over, not only with flowers but with all sorts of veg/produce etc as well. That might cause some confusion if ready-done flowers are delivered and then have to be shoe-horned in around the existing displays.
If the church is decorated with flowers for the wedding and then stripped bare again afterwards, it would be a real shame, as one of the loveliest things about going to church on a Sunday morning is being able to see all the flowers from the wedding the day before.
It isn't just a 'venue' for the wedding, it is a church (as others have pointed out) and I don't actually understand why anyone would want to take all the flowers away with them. Some yes, but not the whole lot...