They tried it in 1803 in OTL with a steam carriage service around London, but it failed because it was more uncomfortable (the heat from the steam engine) and wasn't any cheaper than horse-drawn transport.
For a steam carriage service in London, I think it is more enlightening to look at the the 1830s and Walter Hancock's work. He attempted to start a carriage service with his steam omnibuses for several times, until 1836-37, in the end running regularly for five months and carrying thousands of passengers (according his own calculations his four carriages ran for a total of nearly 4200 miles, with almost 13000 passengers).
I think it can be said he was wildly successful given the constraints of the steam vehicles of the time, achieving a modicum of reliability and an average speed in excess of 10 mph even in longer journies. He even sold one of his carriages abroad, to Austria, thereby inaugurating the history of the export of British motor cars. But, apparently, in economy he could never compete with horse-drawn traffic even if people (and horses) in time become comfortable with his vehicles. The carriages were hand-made with very expensive materials and parts, were frequently out of order and burned a lot of coke and expended a lot of water. Hancock, who had only modest resources, finally had to give up.
Purely from the technical point of view, I would say one could start feeder routes to railway stations in London and other cities successfully from the mid-1830s, using Hancock's models or something close to them and being as fast and reliable as the horse-drawn traffic. But it would be a losing proposition in terms of money and could only be kept up by wealthy (if eccentric) supporters or, say, at the expense of a profitable railway line.
But if it would be kept up, even at a loss, I guess in a decade or two technological progress would make the vehicles slowly even economically viable on their own.
Peg Leg Pom said:
From what i understand steam road vehicles were squashed not by technical difficulties but fear of high presure steam and lobbying from stagecoach and cannal companies.
The way I see it,
path dependency as well as its ineconomy killed the early steam carriage. With all the resources poured to the railways circa 1820-50, the rocket-like (no pun intended) ascent of the railway establishment and even an actual fear (believe it or not) the railway promoters had for a successful steam carriage for common roads undermining their effort, the steam carriage as a tougher technological proposition never had a chance in Britain.
The railway companies quite certainly lobbied against the steam carriage, claiming that any resources used to promote it would be wasted and would hurt their own "great national undertaking". But the canal companies, in the end, were actually rooting for the steam carriage inventors and their supporters, because they quite rightly saw that the railway was the bigger threat. Look, for example, at the anti-railway propagandist Richard Cort, who drew his salary from the canal companies and the stage coach interest but allied in the mid-30s with Alexander Gordon, the persistent steam carriage publicist in public attacks towards the railway companies.
Coincidentally, I posted an excerpt of the inventor's 1838 book on his work with the vehicle in MacCauley's thread
Samuel Morey, or: 1824, with a two-stroke engine. just now. I am due to write an article on the subject by the end of this week, to a small Finnish journal on the history of technology, and I just hang out here rather than work on it...
To be fair, though, it is only a matter of picking and parafrasing relevant parts of my earlier, unpublished texts on the issue.