Do people who want to take their holiday for Hannukah or Kwanzaa, have to take it at Christmas like everyone else?

All companies now have to comply with religious discrimination provisions of the Equality Act 2010.

Wherever it is reasonably possible employers should allow employees flexibility to take leave for their own religious holidays and festivals.

You, or your workplace union if you have one, should ask the company if they have reviewed their policies on taking holidays and the timing of shutdowns at Christmas.