If you've studied contract law then you are probably better qualified than most to answer your own question. There are a few law specialists on here from time to time but I'm not sure how au-fait they are with contract law.
My advice (assuming you are X) would be to send the pound via cheque with a letter stating something along the lines of 'further to our original agreement i hereby enclose a cheque for 1 pound to cover the agreement that In consideration of the sum of £1 and the undertakings given by myself in the Agreement, and your appointment of myself as its non-exclusive licensee to use the trademark on the terms of this agreement provided that such use is not misleading and does not impose or create any liability on Y.
If this is not in accordance with your understanding of our contract, please contact me immediately.'
and put the ball back in their court, so to speak.