I don't know if anyone has said this already but why not just park in the Tesco and walk down the road? I used to do this while visiting the Parking Shop. I'm sure we all did.
The alternative is to take a friend and then turn off the ignition while approaching the sorting office and glide to a stop. Then you get out, pop the bonnet and get your friend to look in the engine while shaking their head in a "oh-no-it's-not-starting" kind of way. While this is going on, you go in and get your parcel. I don't think they can ticket you if the car's broken down. If the council asks why you went in to the sorting office you say that you went to ask for help. Or perhaps you needed to pick up some jump leads that you ordered online.
This is a shocking use of council assets, manpower and time. It is purely a money raising initiative which is specifically objected to by Parliament when CCTV is used for parking and traffic offences. SC are there to serve the people as well as run the administrative needs of the botough and this does neither. I was please to see the current leader of the council post here earlier on...I presume he now has matters well in hand to sort this situation out in what is after all still a democratic country where accountability must be followed through. The buck has to stop somewhere and the parking enforcement team who decides on this must see sense and offer a viable and suitable alternative.
Southwark have 'interpreted' the law as meaning just five minute, but precedents in case law have allowed for waiting for paper work, and finding the right office &c. I think your appeal will be successful at PATAS, but it will cost we tax payers for the luxury of Southwark's contractors causing you to have to spend time & postage on the case. Perhaps APCOA, (Southwark's parking contractors) should be surcharged whenever a PCN is overturned - that might help to focus the Parking Attendants' attention when dishing out (sorry issuing) Penalty Charge Notices.