I missed this one till now...
Like the others said, check the internet for Colleges and training providers in your area for arboriculture courses.
Get started working for someone as a trainee, make sure they are legit, certificated through NPTC/City &Guilds.
You will find several options:
Independant training providers that will offer short courses from three days to a week in the basics leading to NPTC/C&G certificates of competence. Try for one that offers Lantra registered courses if possible.
Some colleges also do these type of short courses and Merrist Wood near Guildford in particular does a ten week course that covers all the basic (and some advanced) principles of arboricultural theory and practical and you come away with all the NPTC/C&G tickets you need to get started and an Open College Network certificate. From this point they have a chap in who helps place people in jobs where you start as a novice groundie/climber continue your learning and then go from there! Or if you already had a job, back to work...
There are continuing options part time after this level, AA Cert Arb. for one.
There are also the longer more formal options - NCH, ND arb, one to two years full time, if you are young enough or have the time, a good route to follow.
Colleges that have a good arb rep Meyerscough, Merrist Wood, Capel Manor, Sparsholt. Any more...?
Good luck, have fun