It’s up to you whether you say anything at work about your caring responsibilities - you don’t have to tell your employer or your colleagues. However, they’re unlikely to be able to give you the support and understanding you need if they don’t know what’s happening.
There are times when it can help if your employer or colleagues know a little about what is happening. For example, if you want to make a flexible working request, your employer will need more details.
You’re likely to need to plan some of your time around the needs of the person you’re caring for, which can be difficult and unpredictable. It can be helpful to talk to your employer about your commitments and concerns.
It may be a good idea to find out more about your employer’s policy for supporting carers before you talk to them about your situation. You can do this by checking your contract, reading your employee handbook or looking at your company’s intranet. You may then wish to talk to your line manager, human resources department, or staff or union representative about what your statutory entitlements are and what other support is available to you from the organisation.