The best way to get involved in aircraft engineering is via the apprenticeship route. The general consensus amongst various leading airlines is that hands on training mixed with theory in a controlled working environment is the most effective.
UK apprenticeships are seen as some of the best in the world and many of the industry leaders started this way. You will generally spend the first year in the workshop and classroom, followed by 2-3 years working for an aircraft maintenance company. At the end of the apprenticeship you will have achieved a City and Guilds level 3/4, and depending on the course, your A1 Licence.
You then have a few choices, you can carry on with your company working as an aircraft mechanic, or you can train further to gain your B1 or B2 Licence. This can either be done on an approved programme where you study the whole engineering course over one year, or follow a modular aviation engineering course where you study while you work and then attend a refresher before taking exams.
Once you have attained your B1, B2 or both, you would then attend a type-rating course which will train you to specialise in a particular type of aircraft maintenance.
These are EASA/UK CAA approved courses. There are in addition many non-approved engineering courses that may be of interest such as EWIS or fuel tank safety.