Well if you look at Lewisham Islamic Centre's website you can see its Muslim primary
school on Lewisham High Street:-
It's very soft not going to be like a weekend mosque school that says all ex-Muslims need to be reminded of their sin, but it will be almost wholly Muslim, why would anyone non-Muslim pay to send their kid there?
The inter-communal group bonds will have to be formed outside of school, which the Islamic Centre will no doubt take the credit for by having a festival days and meal once a year at Eid for outside non-Muslim people.
(I'd say do go to these kinds of events though even if does feel like 'giving support' if only to engage in non-threatening but direct questions to tease out their faith school nonsense, perhaps by pointing out the more faith schools there are the better private schools have an excuse to exist)