OP - you are not being at all clear.
Did you make a formal flexible working request, which was accepted, and then as a result had your employment contract changed to reflect your home working Monday and Friday? Saying it was "logged in ESR" means nothing to most of us.
If so, no they cannot simply revoke it. It would be a change of employment contract. They can consult with you and give notice of the change though.
If not, then it's an informal arrangement. But you could argue it is contractual by custom and practice. This doesn't mean they can't change it, just that they have to give you notice, which I guess they are doing.
If you didn't have it formally agreed, put in a formal request now. The employer cannot turn down your request based on the reason for the request, but don't give them any excuse to try to do so - so don't mention that you take time out for school run and have your child home with you from end of school while you are working (we don't know what age the child is).
I would actually say that a blanket policy to not allow home working could be indirect discrimination. But that is not automatically unlawful. The employer would claim it was a proportionate means of achieving a legitimate aim. And it's not an argument you want to have, frankly. It can only be determined by a tribunal. And they can easily defend themselves by saying "yes, but we consider every flexible working request on its merits, so it's not a blanket policy".