Nick that would be a great idea if you like to gamble. You run the risk of losing the client to a competitor, not getting a job offer from same (not least because if you are behaving so unethically at your current firm they will be wondering if you would do it to them in due course too), and probably getting fired from your current firm for doing it, possibly even getting hit with a law suit thereafter for good measure. And if the firm you are interested is only interested in you because you bring x client with you, what are you really worth if that client goes quiet, they don't secure the business etc etc? The only - and I do mean only - exception to this would be moving at Partner/Director level where the company could reasonably expect a following or book of business to come with you - but the key word here is following, i.e. where the client follows the consultant not where the consultant has solicited the client away from the firm they are leaving.
Aren't there clauses, in black and white, in your contract about this???!!!