IMHO the concept of "parallel construction" is mostly an USA specific thing because USA legal doctrine is heavy on fourth amendment application and "fruit of the poisonous tree" doctrine that can make evidence inadmissible depending on how it was obtained. But all those things and rights are specific to USA, not in general, and not even for other common law countries.
As far as I understand, such "fruit of the poisonous tree" doctrine is not applied in UK, as long as the evidence is believed to be true, it would generally be admissible in court even if it was obtained through e.g. mass warrantless wiretapping, so if they knew who he was already, they could and would have just gone ahead and there would be no need to put in the effort for some parallel construction.
As far as I understand, such "fruit of the poisonous tree" doctrine is not applied in UK, as long as the evidence is believed to be true, it would generally be admissible in court even if it was obtained through e.g. mass warrantless wiretapping, so if they knew who he was already, they could and would have just gone ahead and there would be no need to put in the effort for some parallel construction.