There are post offices and there are post offices
Are the ones offerign the swap service larger branches or ones where there is a counter at the back of another store?
IIRC the LHR post offices are all located within W H Smiths and have different - and shorter - opening hours than the shop that's hosting them.
And of course in the scheme of things there are actually very few old notes floating about due to the long length of paralell acceptance of old and new notes and how ATMs will only be stocked with the new notes very early in the period and banks will only issue new notes to businesses.