I figured that chicken fillets is a euphemism for breast implants.
I figure you're right. In fact, this apparently is a British slang term for implants or temporary enhancements. Armed with your info, I plugged it into google and here we go. Among others, here's a description from one website selling inserts:
Breast Enhancers and Chicken Fillets
Undercover Glamour provides the solution for smaller busted women looking to increase their bust without the risk of surgery. The breast enhancers and silicone chicken fillets are the way forward to giving your life and breasts an added boost. Undercover Glamour offers three different sizes of breast enhancers; from a subtle lift with Mini Voila!, to a confidence boosting extra cup size with Voila!, or for the maximum 'wow' factor with Maxi Voila!
Funny the odds and ends from Doc Martin that drive me crazy. Now that we've answered this important question, we can move on to world peace.