The UK goyernment has been threatening to shut down yeshivos (males) and seminaries (females) for many years to no avail. This isn't new. And they're not merely threatening to defund the yeshivos/seminaries, they're threatening to close down any yeshiva/seminary that refuses to promote acts of toieivo to six-year-olds through twelve-year-olds as an equal and valid lifestyle (regardless of who funds the schools). The goyernment claims the right to dictate the educational curriculum and policy even for those who attended private yeshivos that receive zero goyernment funding. The Chassidishe and Litvishe dayanim have already ruled that schools should be closed rather than comply with this law. Judaism's stance on such an issue is that if the goyernment decrees and mandates Jews to break Jewish Law or tradition (and in particular, sexual immorality), then one must not comply no matter the penalty. Jews are obligated to follow Torah Law, not secular law. If the secular law happens to correspond, that's nice; if it doesn't, then so much the worse for it. If, as in the case here of giloy arayus, the civil law contradicts Torah Law, then a Jew has zero halochic obligation to follow it. Standing firm on the refusal of teaching Jewish children matters of LGBT is a Kiddush Hashem and so funding will find its way one-route or another.
They're not only Chassidish, many (nearly half) are Litvish; others are Sefardish. For this reason, the articles covering the matter use the umbrella term, 'Chareidi'.
The majority of tzdaka/maaser money that makes its way into Chassidishe neighborhoods, including its yeshivos, seminaries and shuls, comes from secular Jews.
There are several thousand Jewish tzdaka/charity societies in the UK alone, responsible for aiding much of the observant community. In any case, the yeshivos will close down before any Chassidishe/Litvishe community allows such toieivo into the secular curriculum. Should the schools close down, others will be open(ed). Yeshivos are accessible to the observant Jewish community the world over, and have been for the last two millennia since Shimon ben Shetach and Yehoshua ben Gamla instituted compulsory Jewish education.