10 years or more ago, there was some legislation passed, I think, which meant that carers were entitled to some time off to do things like taking their caree to appointments - I showed it to my line manager to convince her when I needed to do something like that. I’m self-employed now, so am not sure what the current situation is.
You have the rights to request time off for dependents but unfortunately your employer is not legally bound to agree to it. You have the right to “reasonable” time off in emergencies but there is no legal definition of what is reasonable. Unless your employer agrees to the contrary, the time off is normally unpaid.
However, the mention of Acas does normally keep employers concerned enough to consider your case. It might be worth asking the Acas Helpline for advice.