Which is the smallest or quietest services?
This question is more complicated than it ought to be.
If we take "motorway services" to mean any service station that is signposted from a motorway (as we do), then Old Inns (on the M80) has little more than a petrol station. This means it is likely to be both the smallest and the quietest.
It's that simple, but people don't like that answer because Old Inns was never intended to be a motorway service area, it's a petrol station that had a motorway built next to it. If it were just an A-road site as intended, it would be pretty average.
Of the motorway service areas that were always intended to be one, Severn View on the M48 has a tiny building and low trade, but it is built on huge grounds. The winner is likely to be back in Scotland: Kinross on the M90 can be quiet, and the building at Bothwell on the M74 is smaller but built on larger grounds.
Special mentions should go to Cullompton, which is the smallest service area to be on a very busy motorway - the M5 - and also to Pease Pottage which started out tiny but has grown to become huge.
Finally, Appleby Magna is signed from the M42 and is only marginally bigger than Old Inns - but those signs do say that Appleby Magna is not a motorway service area.
On A-roads, as already stated, there are a few small ones. One of the smallest to receive full signage is Great Ponton, which surprisingly is on the very busy A1: as recently as 2022 it was basically some fuel pumps with no shop. In terms of trade, Leicester Markfield is virtually derelict, but does have a lot of land under all that foliage.
As for the quietest single day: if you rule out issues caused by road closures or other traffic issues - it's almost certainly going to be Christmas Day or New Year's Day, probably in the 1960s. March 2020 would have come close to this.
See also: Biggest, Facts and Figures