Deliveroo is acting as the agent for the delivery service, doing business on behalf of Deliveroo, not Waitrose…at least that’s how I read the words “act as your agent to solicit, promote and conclude contracts for Delivery Service orders in your name and on your behalf, and to collect customer payments owed to you in respect of those orders.” The “your” is the delivery service, not you. You are labelled as “the customer.”
The whole paragraph is about Deliveroo acting as the agent for the delivery service that actually brings you the groceries, and them taking the money from you, not the delivery services taking it from you.
Deliveroo will have a similar contract with Waitrose that ensures Waitrose gets the money collected, minus the agency & delivery fee.
In essence, it’s almost like you didn’t actually do business with Waitrose, but with Deliveroo. And, in turn, Deliveroo is a middle man market maker for Waitrose on one end and the actual delivery service on the other, if that makes sense?!