It's true you'd be on a sticky wicket. I can't see anything about not using them with the engine running, but Reg 27 of the Road Vehicle Lighting Regs says a work lamp must not be:
"Used so as to be lit except for the purpose of illuminating a working area, accident breakdown or works in the vicinity of the vehicle".
so you'd need to convince the copper that the area being illuminated by the lam was a "working area", which might stretch credibility a bit!
Interestingly, although the regs limit the wattage to 24 Watts apiece, there is no requirement for intensity, so I would have thought we could get some very bright LED bulbs that were well within that power rating. I suppose that would invalidate the approval requirements for the lamps though. (they need to bear an approval marking if the vehicle was firs used after 1986).