How efficient was the postal service in England in the 1830s?
For example, is it possible to estimate how long it would have taken for a letter to arrive if sent by a standard service from London to Nottingham in the 1830s?
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I don't know about London to Nottingham in particular, but the fastest mail was transported on dedicated mail coaches. These saw improvements in speed thanks to better roads...
The following is from Her Majesty's Mails, William Lewins, (London, 1865), pg 145
Most of the post-roads were macadamized before the year 1820, and it was then that the service was in its highest state of efficiency. Accelerations in the speed of the coaches were made as soon as any road was finished on the new principle. From this time the average speed, including stoppages, was nine miles an hour, all but a furlong.
In terms of example travelling times, it goes on to list the following...
The fastest coaches (known as the "crack coaches" from this circumstance, as also from travelling on the best roads) were those, in 1836, running between London and Brighton, London and Shrewsbury (accomplishing 154 miles in 15 hours), London and Exeter (171 miles in 17 hours), London and Manchester (187 miles in 19 hours) and London and Holyhead (261 miles in 27 hours). On one occasion, the Devonport mail, travelling with foreign and colonial letters, accomplished the journey of 216 miles, including stoppages, in 21 hours and 14 minutes.
"Early-to-middle 19s century" is a bad time interval for this question, because it is evident that dramatic changes occured DURING this period, with the introduction of trains.
It is not surprising that the speed of delivery depended on the destination. Within (greater) London it was possible to exchange several messages in one day.
For delivery times to other destinations (in the middle of the 19th century) see this:
EDIT: In the very end of this text one can read for example:
Letters, however posted in London and sub-districts between the hours of 7 and 9 p.m. on Saturday, are forwarded to the travelling post-offics, and reach their several destinations in time for delivery on Monday morning.