But he would have needed to bring contempt onto the uniform for that to apply. Parading, even in uniform that wasn't his, doesn't fit the criteria for contempt, he obviously had high regard for the uniform hence why he pretended it was his.
By falsifying his service and professing his decoration he is treating the uniform and the Act with contempt.
That and simply wearing it, or any such distinctive marks of it, is illegal under the law in the first place.
This Act may be cited for all purposes as the Uniforms Act 1894.
2 - Military uniforms not to be worn without authority.
(1)
It shall not be lawful for any person not serving in Her Majesty’s Military Forces to wear without Her Majesty’s permission the uniform of any of those forces, or any dress having the appearance or bearing any of the regimental or other distinctive marks of any such uniform: Provided that this enactment shall not prevent . . . any persons from wearing any uniform or dress in the course of a stage play performed in a place duly licensed or authorised for the public performance of stage plays, or in the course of a music hall or circus performance, or in the course of any bona fide military representation.
(2)
If any person contravenes this section he shall be liable on summary conviction to a fine not exceeding level 3 on the standard scale.
3 - Penalty for bringing contempt on uniform.
If any person not serving in Her Majesty’s Naval or Military Forces wears without Her Majesty’s permission the uniform of any of those forces, or any dress having the appearance or bearing any of the regimental or other distinctive marks of any such uniform, in such a manner or under such circumstances as to be likely to bring contempt upon that uniform, or employs any other person so to wear that uniform or dress, he shall be liable on summary conviction to a fine not exceeding level 3 on the standard scale, or to imprisonment for a term not exceeding one month.
4 - In this Act—
“Her Majesty’s Military Forces”has the same meaning as in the Armed Forces Act 2006;
“Her Majesty's Naval Forces” does not include any Commonwealth force.