It's not hard to find lists of employment and recruitment agencies in the UK, with numerous lists available online. Which agency you go for depends on your specific needs.
It is recommended that you thoroughly research the available options before choosing two or three agencies to approach. You can research agencies online via online directories that provide information daily.
When you identify the right agency for you then further research on their own website is advised. You can also look at job adverts in newspapers, specialist publications and on jobs websites, before investigating further.
However, it is worth noticing that many agencies do not need to advertise their jobs. Ask friends, colleagues or business contacts which employment agencies they would recommend.
Someone may have already sourced a new job through an agency and be able to recommend on to you. Asking Human Resources departments which agencies they use is also a good idea.