There are a lot of problems in this area right now, the government are giving families 15 hours free education in the term after their third birthday.
However, and it really is a big however, many independent nurseries genuinely cannot run only on that income. If it is in a state nursery class attached to a school, the school subsidies the provision, but not in a privately run setting.
There are loop holes, and yes settings can charge a top up if they use the loopholes. Where I work, the council have people employed to work them out, because there is no way the council can put every child into 15 hours free education, as there aren't enough state nurseries.
Sadly the change in conditions has been enforced on them, this is not just to squeeze money out, in many areas, this is to stay afloat. Settings are closing - I know 3. And they had to wait until after the election because it was undecided: Tories wanted the funding cut completely, Libs want to keep it. It is very late in the day ( imagine how your provider is coping )
One option is to phone the council who have to offer you 15 hours free education, but that could be at any setting in your borough.
HOWEVER, settings only have to offer 15 hours free education ( plus top ups if necessary for extra time/ provision ) you are parents don't have to take it. The funding is paid pro rata, so they can attend 3 sessions a week and still claim the funding.