My employer will not promote me because I have elderly relatives and they are worried that I will have to take time off in the future to look after them. Is this unlawful age discrimination?

The age regulations do not protect you in this situation, although you may have a case under sex discrimination law. However, this is an area of uncertainty as to whether the age regulations comply with EU law. You should ask for support from your union representative if you have one and get some expert legal advice.