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 the smallest (both by the main building size and by its overall grounds), and it's likely to be 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.
Some other answers that may go down better:
- Severn View on the M48 has the second-smallest building in the UK, and the smallest in England. It's built on huge grounds.
- Kinross on the M90 is believed to be the second-smallest by total grounds.
- Bridgwater on the M5 is third by this measure, and the smallest in England. It also sticks out for being a lot busier.
- Cullompton has bigger grounds but a smaller building than Bridgwater, but sticks for the same reason.
- Pease Pottage started out tiny but has grown to become huge.
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