Actually the service could have been carried out by the British Forces Postal Service by the Royal Engineers. I found this.....
Nelson beat the French and Spanish fleets at Trafalgar on October 21, 1805.
Lieutenant John Richards Lapenotiere took his dispatch from Falmouth to Whitehall in 37 hours, arriving at the Admiralty at 1am on 6 November.
He made 21 stops to change horses, each of which will be marked by a plaque.
His detailed expense account shows that he followed one of the well-known routes to the capital, changing horses every 10 to 15 miles. He made 21 stops at coaching inns in Truro, Fraddon, Bodmin, Launceston, Okehampton, Crockernwell, Exeter, Honiton, Axminster, Bridport, Dorchester, Blandford Forum, Woodyates, Salisbury, Andover, Overton, Basingstoke, Hartfordbridge, Bagshot, Staines and Hounslow. At some stops he had to change post-chaise, as different operators covered the various sections of the route. He arrived at the Admiralty in Whitehall at 1.00 am on 6 November, having travelled the 270 miles from Falmouth in some 37 hours non-stop - an amazing feat. A stage coach usually took some 4 days to do the journey. Amazingly, Mr William Marsden, Secretary of the Navy, was in his office when Lapenotiere arrived. The news of victory and tragedy spread through London and the rest of the country.
http://www.themapshop.co.uk/images/OS%20Button s/montage2.jpg