the UK slowly, peacefully changed

This isn't always necessarily the case. The Representation of the People Act 1832, usually known as the 1832 Reform Act, passed against a background of widespread popular violence.

The Act was designed to implement a number of reforms which would greatly increase suffrage and representation in parliament, in particular by abolishing so-called rotten boroughs and implementing a series of new parliamentary seats to bring constituencies into line with the new demographic geography of the UK. 'Rotten boroughs' were typically older constituencies which had been left behind by the rapidly changing population distribution affected by the industrial revolution, but which retained their parliamentary standing despite often having very small populations. This in turn meant that these boroughs could be easily controlled by landowners and landed gentry, who then had a disproportionate say in Parliament. Of course, this meant that rapidly-growing industrial cities with large working class populations had little or no representation. Boroughs also had no unified rules on the criteria necessary to vote, which often meant that large sections of the population could be seemingly denied a say on a whim. In the major industrial port of Bristol, for example, only 6,000 people of a population of some 104,000 had the right to vote.

While the Reform Act didn't seek to enfranchise the working class - you still needed property worth £10 to register to vote - it took great steps towards standardising the rights of voters, and did significantly expand the numbers of middle class voters [The Representation of the People Act 1867 would actually greatly extend suffrage to working class men in the UK]. Naturally this redistribution of power away from the landed elites faced stark opposition from the House of Lords and many of their tenant Members of Parliament - particularly among the Tories, and the bill failed its first reading in 1831 despite massive public pressure. After an election swept the Whigs to power in all but the rotten boroughs, the bill passed its second reading but was struck down by the House of Lords in October 1831. This was met with widespread public violence.

Rioting and violence broke out across the Midlands, the South West and Dorset, in response to what was seen as the self-interest and corruption of the Lords. In Derby, a mob stormed the jail, and in Nottingham, rioting crowds burned down Nottingham Castle and ransacked Woolaton Hall, homes of the Duke of Newcastle and Lord Middleton respectively. The worst of the violence was in Bristol, which was particularly significant given the city's position as one of the most economically important ports in the country. Rioters laid siege to the new assize courts and the mayor's house, and chased a local magistrate through the streets. The house of the Bishop of Bristol - who had voted against the bill - was attacked and burned down, with popular legend in the city claiming he was forced to escape across the rooftops in his nightgown from the flames. Other wealthy houses were attacked and looted, including the mayor's mansion, and parts of the city jail were even demolished. Eventually the army was called in to end the rioting, leading to the deaths of 4 people and the wounding of some 86 more, although more are thought to have died in the fires set by the rioters. The officer in charge of dispersing the rioters later shot himself.

The violence led to widespread outcry and fears of repeat performances if the bill failed a third time. With parliament prorogued for the coronation of William IV, the Whig government tried to cram the lords with newly-enobled pro-reform lords, but the new king baulked at taking such a drastic and overly political action so early into his reign. As the Prime Minister resigned in protest, there was widespread fears of violence and even revolution, and there was a run on the Bank of England with almost a third of its gold stocks being withdrawn. Parliament was swamped with petitions in favour of reform, urging the Commons to deny funding for the government, and even calling for the abolition of the monarchy and the peerage. With the Duke of Wellington unable to form a Tory government, the opposition relented, with the Whig Lord Grey being returned. Wellington in turn wrote to Tory Lords, requesting they allow the passage of the bill to avoid losing their power by having the Lords swamped with Whigs, and to avoid further bloodshed on the streets.