I would agree with Gordon in that there is nothing illegal in having the picture
itself up on the website. The IP rights to the picture will probably be assigned to the company that commissioned it. And there may well be a clause in the subjects employment contract which gives permission for their image to be used in publicity materials. Even if there's not there's an implied permission if they posed for it to any degree...
The only 'lever' is that if there's text or something else that implies this person's services ARE available from this rival; for instance if the image appears on an ' our staff' page. But if they're simply seen in a banner (for instance) doing their job then I'm almost certain there's nothing you can do about it. Certainly we've had disgruntled employees try to force our clients to have them removed from training and promotional films etc to no avail.
Depending on circumstance Trading Standards might be in a position to point you in the right direction, it's also possible this might be an ASA issue (
Advertising Standards Authority) but I suspect a solicitor's letter might be the lever needed.