Does the UK not have a similar law against misrepresenting one’s military background?
Wearing decorations to which one is not entitled is an offence in the UK under the Army Act of 1955. Three months imprisonment per count is the sentence, I believe.
The thing is - he’s pretending to be SAS and that makes it tricky. As a matter of policy the British government virtually never comments on the SAS, either to confirm nor deny anything. That policy would have to be broken to prosecute. If you go around saying “John Smith was never in the SAS” what do you do when a newspaper threatens to expose a real former SAS soldier whose identity needs to be protected.