As with all self-employed individuals residing in the UK or Ireland, cat sitters are responsible for complying with their local tax and regulatory framework that applies to self-employment.
If you wish to obtain first-hand and accurate information that relates to your query, we would recommend you check the official governmental website for all matters related to self-employment and taxation.
Here are some useful links:
An overview page on being self employed which is an excellent introduction on what you need to do:
For more in depth information there is an e-learning course that is extremely useful: http://www.hmrc.gov.uk/courses/SYOB3/syob_3/html/syob_3_menu.html
There are also webinars (online seminars) and YouTube videos that can be found here: