Since then I have also noticed rust around the barrel and mono block joint. Would I be within my rights to ask to have the shotgun replaced under the warranty?

Shooting legal advice
Under the Sale of Goods Act, goods (and this includes guns) must be fit for purpose and of reasonable quality.

The normal remedy if a defect arises is for the vendor to repair it and if he can’t do so satisfactorily the purchaser is entitled to a replacement or refund.

This would seem to cover the opening lever and firing pin issues but if they fail again I believe a refund or replacement is a reasonable request.

The rust issue is more difficult to advise on without knowing the gun better.

Usually rust on a gun would be the result of some sort of neglect.

However it is possible there is a design fault which makes it difficult or impossible to clean and oil the gun properly in which case a refund or replacement would also be reasonable.

If a gun is inherently prone to rust due to a design defect a refund or the offer of a different model is the best course of action.