I think part of the problem is that you need to disassociate the idea of an 1848 revolution with events in Britain. I'm not saying there was no revolutionary potential in Britain, far from it, but the circumstances that fed 1848 in Europe were very different to the ones shaping Britain at the time.
Your biggest chance for a sort of popular uprising would be in the harsh years of the 1830s, particularly the harsh winter of 1831-1832. There were massive problems with food supply, with agricultural unemployment, with industrialisation replacing workers in cities, and political repression. This BBC page by Prof. Evans is useful to provide context:
http://www.bbc.co.uk/history/british/empire_seapower/revolution_01.shtml
People like to roll out King Ernest or the failure of the Great Reform Act, but really they are unnecessary. The nation was already on the brink of crisis in this period without any of those alt-history ideas. You just need, as Prof. Evans points out, the House of Lords and/or William IV to be more difficult or obstinate, radicals not to back down, the Swing Riots of 1830 to get worse or urban unrest to grow, and the powder-keg could be lit.
As for what it would look like (this is, of course, on the basis of a lack of compromise which is far more likely):
* It could be a coup d'etat, as
@Whiteshore points out, but its more likely to look like the 1830 or 1848 revolution in France. A lot of unrest, across the country, in both the countryside and cities, but the decisive action coming in London. Riots in Liverpool or Manchester or Bristol (all major cities at the time) might prefigure this, but London would be the tipping point. Events in the period (Peterloo, suppression of the Swing and Rebecca Riots, etc) proved that sections of society and the military were more than willing to use violence to protect the status quo, so there would be fighting in the streets. Likely the Royal Family would not stick around to wind up like Louis XVI but flee the country to France).
* The Commons would assume ultimate priority over the country, and possibly accept universal manhood suffrage in line with later Chartist demands. There would be tremendous pressure to repeal the Corn Laws and, depending on the date, the New Poor Law.
* Like in 1848 there would be tension between the radical and liberal wings of the revolution, with the liberals probably winning out as they promise a more realistic and stable financial position. Working people, and their champions, would call for but likely not get workplace reforms, land redistribution, guaranteed work etc etc.
Long Term:
* Political instability as the shape of the new state is determined. Britain suffers financially and developmentally (this is at a crucial point for the railway revolution which needs stable investment).
* British politics may well polarise into a Liberal-Radical vs Conservative-Monarchist split akin to much of the continent.
* The European balance of power is destabilised and the future of the colonies, India, and the USA all changed as a result of disruption of British power, emigration, and investment.
* Don't discount the appeal of a restoration, popular or forceful, by the monarchy at a later date.
* It is highly unlikely - I really think this - that you will see the monarchy go to Canada/Australia/India. I know this is a favourite of people in alt-history, but it really is a cliche with very little historical basis.
That's my pennyworth, anyway. Hope it helps.