If you find yourself caring for another person and you both feel that, if necessary, you should be able to take control of their affairs, you could suggest that they give you a 'Lasting power of attorney for property and financial affairs' (LP1F) and a 'Lasting power of attorney for health and welfare' (LP1H). If they agree, you could then be legally responsible for dealing with their assets and financial interests as well as making decisions about their personal wellbeing. Without these documents, you won't have the right to do this, even though you are acting as a carer. You can't, under any circumstances, force the person you care for to sign an LPA. They must willingly sign it and must be of sound mind to undertake it; otherwise it will be ruled invalid.
There may be a natural reluctance to pass over control of their affairs. You could ease their concerns by sharing leaflets from the Office of the Public Guardian (OPG) with them, such as Making decisions about your health, welfare or finance. Who decides when you can't? (opens a PDF).
If the person you care for is unable to draw up an LPA (perhaps because they don't have the mental capacity to do so), you can apply to the Court of Protection (COP) to be appointed as a deputy. The deputy is a person appointed by the COP with ongoing legal authority to make decisions on behalf of another person who lacks capacity. For more information, see What is a deputy?
In most cases, you will want to make decisions on an informal basis, rather than applying to the COP. Where there is a disagreement, it's important to remember that under the Mental Capacity Act (MCA), a person should be assumed to have capacity to make their own decisions, unless it can be shown that they lack capacity. This means that even if you don't agree with a decision of the person you care for, you must allow them to make that decision, unless it can be shown that they lack capacity to make that decision. You can, however, try to persuade the person you care for to see your point of view.
The MCA outlines what responsibilities you have towards the person you care for and the Code of Practice sets out the best practice to follow. To learn about your responsibilities under the MCA you should read the guidance published by the OPG. Its guidance can be accessed with the following link (opens a PDF): MCA Code of Practice
For more information, see the What is mental capacity? section.