Under English law consideration needs to be paid to make a contract valid.
The reason for that is that both parties are meant to get value from a contract, it wouldn't be enforceable otherwise.
So paying £1 ensures that the party who for e.g. assigned their intellectual property to the company in an IP Assignment agreement is getting something in return (i.e. £1), they're not doing it for nothing.
So the contract included wording to say that, in this case, the company agrees to pay the other £1 at the time they sign the agreement, and the other party agrees that the £1 has been received by them (whether you actually pay it or not is up to you, the point is that you both agree it has been paid).
This consideration, as it's known, used to be a peppercorn, now it’s a pound – some fun reading here.