As pretty much everyone else has advised, finish your degree. You may be surprised how many jobs open up with that, and "office" jobs in this business don't tend to keep you behind a desk for very much of the day. Aviation engineering is very much real world based and you will find you're out and about and talking to the people twirling the spanners as a matter of course.
If you are determined to go hands-on read this as a starting point:
http://www.caa.co.uk/docs/33/ELGDBook_07_WebVersion.pdf
NOTE the ELGD has now been superseded but if you google round it you can find the regs. It remains a good basic guide to the requirements to become a licensed engineer. In your case without an apprenticeship you are looking at passing the modular exams plus accumulating 5 years hands-on experience recorded in the CAP741 log book. If you can get on the books of a contract agency you can get the hands-on stuff going, don't bother applying to airlines direct as they are all cutting back. Going connie is the safest bet as long as you're prepared to be flexible where you work. The first step on the ladder is hardest so maybe find a local flying school in the uni holidays and offer to help out for free in return for some spannering experience. Once you're working you can study for the exams, I did mine at Barry College self study, just bear in mind there is a specified window of validity to complete them.