There is no union, and most jobs are filled with existing network unless you can walk onto an agent's books. You should also establish your ability to work in the UK - it isn't very straight forward unless you are an EU citizen. There are probably short term visas, especially if you are a student/of student age.
London is a very saturated market and most people without an existing network work for around 2 years unpaid in order to build a network.
Just checked your portfolio, if you have lots of evidence of your SFX work, you should contact SFX houses here in advance. They tend to be pretty fair in that they will take on clearly talented people if they have vacancies.