Questionable gcse grades for medicine.

I have spent a month in Cambridge with a summer programme and I completely fell in love with it!
I've known from very little that medicine would be a dream come true for me but I haven't really achieved the grades I should be dreaming of too. Perhaps I was young and lazy...

GCSE GRADES:
A in Maths
A Modern Greek
A Physics
A in Biology
B in Chemistry
B in Geography
B in Human Biology

I haven't yet taken any A-level exams and since now they are back to linear, I will be sitting Bio, Chem and Phy along with maths in 2017.
I do already though have an A in the Greek A-level.
My GCSE B's where really close to the A grade.

All I want to know is,
Can I still give it a try and apply to Cambridge or just forget about it?