Work experience for Graduate entry medicine in London

Hello everyone,

I am currently a student on placement, studying biomedical engineering, I will hopefully graduate in 2017 with a first. I recently heard of a graduate entry in medicine, and I am quite interested (as I imagine hundreds of other people are...). I have been offered a place in medicine in another country in 2012, and declined it for personal/economical/political reasons, and I am regretting it.
I would just like your opinion/ advice. My real issue is that, as I come from a french background, I didn't have much chance in getting any work experience, well at least not in a medical field. But I have talked to doctors, and to medical students, and I did spend nearly a month if not more in a hospital and caring for a parent. I obviously know this cannot be considered as 'work experience', but just to show that I quite understand the reality of becoming a doctor.
I am currently doing a placement as an electrical undergraduate engineer in the energy field (1 year) and that is the only experience I have. I was thinking that maybe if I started a volunteering work in september before applying in october that might help?
I obviously know that I need a lot more than just work experience, but that's the bit I am the most insecure of.
So I just wanted to hear from you, do you think I would have a chance or I should just let it go?

Thank you so much!