In the UK, they do not have the Fruit of the Poisonous Tree doctrine. Parallel Reconstruction is not needed to bypass admissibility constraints because those constraints don't exist in the first place.
Parallel Reconstruction is used to avoid scrutiny of the original source of evidence. Even when used to legitimate ends (and I have doubts how often it's used as such), there are fundamental problems with dodging accountability.
Parallel construction is still used in the UK. That's my point - it is used to conceal sources in a wide variety of circumstances, and is orthogonal to any issues regarding illegality of evidence.
Parallel Reconstruction is used to avoid scrutiny of the original source of evidence. Even when used to legitimate ends (and I have doubts how often it's used as such), there are fundamental problems with dodging accountability.