Sign language is not the same all over the world. In fact between different towns or regions of England the variation can be enough to cause problems - maybe because TV and radio do not have the same influence over BSL as they do on English.
BSL (British Sign Language) is the first language of around 70,000 people in the UK. I began learning it in 1998 after meeting deaf people in Bogarts. It is easy to find classes that teach stage 1 BSL, which gives you a basic grounding, and a certificate from the CACDP, if you pass the examination at the end of the course.
Probably every sign language has to uses a lot of finger-spelling (using a manual alphabet to spell out a word or part of a word). Obviously finger-spelled words are not usually international. If you would like to learn the BSL alphabet see the Wikipedia BSL alphabet image.
There are at least two other sign languages in use in Britain:
SSE (Sign Supported English) uses English grammar (BSL grammar is quite different), with a signed equivalent of every word in the corresponding spoken or written English sentence. It is often used to teach deaf children English.
Link is a language used by deaf-blind people. Signs are made on the hand of the other person. The deaf-blind alphabet is similar to the BSL alphabet, and is easy to learn here. Peterborough is home both to Sense and DeafBlind UK.
BSL is distinctive because its manual alphabet uses both hands to spell letters. Most other countries use a one handed alphabet. Here is a link to the American Sign Language Alphabet. I guess the BSL alphabet is easier to learn and sign, but possibly not so easy to read.