In the US military this sort of thing is possible. A Colonel calls up a manufacturer, hammers out a deal, and the deal gets done. Manufacturers are always interested in making more money, so I can easily see a manufacturer saying "sure we can do that, and here's what it will take to make it worth it to us".
When you think about it all the manufacturer did was run the cloth through a dye bath before assembly. Not a big deal and certainly within reason for a unit to afford. Having the uniform construction significantly altered, on the other hand, would likely be beyond what a unit could afford. Heck, it looks like they found a custom thread color wasn't in their budget, not to mention button color change! I can also see MoD being involved even if just to give it's blessing.
It really depends on how much flexibility there is within the British procurement system. I have no idea so maybe my theory holds no water.
BTW, I have a factory made overdyed US Army UCP jacket. So it seems the US and UK both played around with this. Very rare and in this case they did change the color of the velcro and (IIRC) the zipper. But otherwise bog standard jacket and labels.