The UK now has UWOs - so for the largest cases (they probably don’t care so much about smaller transactions) they could probably find out through serving a UWO:
An unexplained wealth order (UWO) is a type of court order issued by a British court to compel the target to reveal the sources of their unexplained wealth.[1] UWOs were introduced by sections 1–2 of the Criminal Finances Act 2017 and are governed by sections 362A–362T of Part 8 of the Proceeds of Crime Act 2002. Persons who fail to account are liable to have assets seized after an enforcement authority, such as the National Crime Agency (NCA), makes a successful appeal to the High Court.