The exact location of Hogwarts isn't specifically known, but we do know that it's in Scotland. If we take the most likely location, (near Argyll and Bute) that places it some 500(ish) miles from your destination in London.
Assuming your carriage is drawn by mundane horses, replenished en-route and you don't mind getting up early, you'll make about 30ish miles in a day or a total journey time of about 15(ish) days.
Since that means an effective round-trip of a month (excluding any time spent at home), I'm at a loss why you wouldn't use one of the many faster alternatives available to wizards.
Wizards who cannot Apparate (dematerialise and reappear at will), who wish to travel by daylight (meaning that broomsticks, Thestrals, flying cars and dragons are inappropriate), or whose destination has no fireplace (rendering Floo powder useless) will have to resort to the use of a Portkey.
Portkeys By J.K. Rowling
If you're desperate to have your character in a carriage for some reason, there are also better options than horses.
And a muggle train on the newly opened Caledonian line (available after 1850) would take you just 13 hours to get from Scotland to London at a much cheaper ticket price than a carriage.