It is an offence to obscure a registration mark in any way or make it not easily distinguishable.
Section 43 of the Vehicle Excise and Registration Act 1994
43 Obscured registration mark.
(1)If a registration mark fixed on a vehicle as required by virtue of section 23 is in any way—
(a)obscured, or
(b)rendered, or allowed to become, not easily distinguishable,
(2)A person guilty of an offence under subsection (1) is liable on summary conviction to a fine not exceeding level 3 on the standard scale.
It also looks like the rear lights are obstructed. To carry it like this you are going to need a 'towing board' with lights and number plate on.
Cut him some slack. Is the car being driven? No. Is the car even on the road? No. For all you know OP fits a lighting board before he actually drives the car like this - I know I wouldn't bother fitting one just for this guide!