I don't think that a transfer of undertakings arises here. It arises when there is a genuine and definite change of employer.
In your case, the client has decided to take their business elsewhere to another company. You are an employee of the consultancy firm NOT the client who contracts with the consultancy firm.
If A employs B and A sells his business to C, B then becomes an employee of C - a transfer of undertakings arises.
As far as I can tell, you are still employed by A and are entitled to nothing from C.