The former order was placed on Saturday 21st, and I elected to use "Delivery Method: FREE Super Saver Delivery". It was despatched mid-morning on Monday 23rd by Royal Mail, and arrived just before 10am on Tuesday 24th.
After I'd read some of the stuff in that former delivery, the latter order was placed in the late evening on Tuesday 24th, and I elected to take "Delivery Method: First Class", hoping that it would be sent using Royal Mail's First Class service as detailed on this page. Instead it was despatched an hour or so ago by City Link.
There's no suggestion anywhere that when I'm offered the choice of "First Class" that they'll decide to send it via some other carrier instead.
If I'm not in (as is frequently the case) my parcel should be at the Royal Mail parcels depot just under a mile away, but instead it'll be at City Link's depot 24 miles away.
Amazon just might possibly be idiots.