Richard,
You would seem to have got there before me, as I had also thought of comparing Nelson's last journey with that of Lapenotiere's after Trafalgar – which would seem the obvious comparison, short of anything else.
It might also be worth considering the average distance between stops, which perhaps give some indication as to how far a team of horses could comfortably travel before they needed to be changed. I would imagine there were rules and conditions laid down for this. A look at the Ordnance Survey Trafalgar Way Map, shows the places where Lapenotiere changed horses and these would seem to be roughly about ten or twelve miles apart on average, give or take. Some stretches between changes are considerably longer (particularly over the moors and other sparse areas), and others shorter.
Conveniently, the map also shows Nelson's last journey from Merton to Portsmouth. However, and using the same criteria, I find it hard to believe that Nelson stopped only the once, at the Anchor in Liphook, although this appears to be the only one mentioned, as far as I am aware, in hard fact – but obviously not in myth! It is of course accepted that Lapenotiere was travelling as fast as possible, and covered the distance in a shorter time than the average mail coach (thus more stops were probably needed) but presumably Nelson was also travelling relatively fast.
However I still think as do you, that a stop at Burford Bridge was unlikely and incomprehensible, as it is well off the London-Portsmouth road and, as you have worked out, would have put 22 miles on the journey. 10 mph would seem rather fast for a sustained speed, but between 8 and 9 seems more reasonable. If Nelson left soon after dinner as is stated, say at 10pm, I make it that he would have averaged 8.5 mph on the road to get to Portsmouth by 6 am the following morning. If he left an hour earlier at 9 pm, he would have averaged around 7.5 mph, close to your figure for Lapenotiere. The latter figure would seem the more likely, allowing for changes of horses, etc.
It had crossed my mind that a stop at Burford Bridge might only have been possible, if Nelson had not begun his journey on the Portsmouth road, but instead taken other local roads to Burford, before joining the main route afterwards. However, these roads would presumably have been smaller and bad, and with the added risk of getting stuck. They may well have also been the haunt of highwaymen. I think we can dismiss this possibility, as I can't imagine his Lordship would have taken that risk – and he would have wanted to get to Portsmouth as quickly as possible.
Regarding the 'sextant', it is more likely to have been a quadrant, which I believe was the more common instrument at that time. However, to the uninitiated they are all sextants, which is the instrument used today. I also asked myself, 'how many does Nelson possess?' Since he was an Admiral, he would have hardly needed one in any case, since his sun-sighting days were probably over, and he relied on other junior officers for that information! I have a picture in a book of Nelson's quadrant, which is credited as being in the RNM at Portsmouth – although of course I can't say where it was before that!
