Sticky wicket, would that be the right phrase? I don't know what laws may apply in the UK, but on the side of business etiquette and ethics, it might be worth speaking with your existing client first. If they perceive you've gone behind their back, they may be angry enough to drop you. A few extra pounds from the new player may not be worth that loss to you, whether you have the legal rights to do so or not. There was once a safe driving advert in the US about being cautious and driving defensively, because "You could be right, dead right". I do mostly advertising photography, and many times what I photograph is proprietary to the company. My reselling it for other uses without written permission would very likely be a deal breaker for future work. If they took me to court over it, I could probably defend my copyright, but at what other cost?
There's also the question of "Do you have a contractual agreement, and what does it say?"