If you wish to accompany your employer to the UK as a domestic/household worker, you will need to apply for a Domestic Worker visa. You can apply for this type of visa if you have been working for your employer for at least one year. You will most likely be granted a visa for between six and 12 months, depending on the length of stay of your employer. This visa can also be extended.
Once you gain entry to the UK you may change jobs as long as you continue to work as a domestic worker in a private household. If you intend to change jobs you must inform the Home Office of the change but you do not need to make a formal application until you need to apply to extend your original visa.
If you come to the UK with your employer on a visit then you are expected to depart with them. If you stay longer, you are not allowed to work unless members of their close family are also visiting and they want you to work for them. You must, however, leave at the end of your permission to stay.
If your employer is living in the UK and takes trips abroad, you do not need to go with them as long as they are still based in the UK and are going to return.
If your employer leaves the United Kingdom permanently, you are expected to leave with them. If you do not, you must make arrangements to leave the UK before your permission to stay ends.