Ok, so the first letterpack I sent arrived in two days, although it was promised by close of business the next day. Post Office to Parcel Force to FedEx. Cost 52 pounds. Sent the second one the same way, based on the Post Office clerk insisting it should have arrived next day, and apologizing. Same cost, same result.
Put in a claim for the first letterpack before having sent the second with Parcel F.. Stated I was told it would be there next business day and it did not arrive, asked fora refund as the service was mis-sold/misrepresented based on what the Parcel Force phone lady later told me (there is no such service) when I called to inquire about the second letter pack.
Parcel Force came back with basically "yes there absolutely is next-day, but since your receipt is time-stamped 13:34 and our pickup cutoff is 13:30 we are denying the claim." I appealed, saying I'd been in the counter line for a half hour, and that no Parcel Force courier came in to pick anything up, and I'd been at the counter filling out the paperwork when it hit 13:30 and was told it was going out on time. So then I got a response to my appeal saying it had been granted and they're cutting a check that should be here within seven days.
I then asked them if they needed for me to put in a separate claim on the second shipment (I'd send them both receipts when they asked for them, as by that time the second letter pack had the same fate) which was time-stamped at about 11:00am or if they were going to include it in the check. Have heard nothing back yet.
This country is crazy with a generic low-level incompetence.