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The existing answers provide an excellent background to the political situation in the nineteenth century. I will try to answer the specific points raised in the question.
Before I begin, I would like to clarify a few points.
Firstly, the ability of the monarch to dissolve Parliament comes under what is known as the Royal Prerogative. Since the "Glorious Revolution" and, in particular, the 1689 Bill of Rights that followed it, the exercise of Royal Prerogative has been limited. Article 1 of the Bill of Rights states that the:
"power of suspending the laws or the execution of laws by regal authority without consent of Parliament is illegal."
Further, the Bill of rights confirmed that Parliament had the right to limit the use of remaining prerogatives (which they did in the Triennial Act of 1694).
In practice, this meant that the monarch could no longer dissolve Parliament without the consent of Parliament. (There was a specific exception to this however. Parliament was dissolved on the death of the monarch, as happened in 1820 for example, although - to be fair - this is very much an extreme case!)
The second important point is that, in the nineteenth century, the monarch appointed the Prime Minister and had the absolute right to appoint whomsoever they wished. Obviously, this could - and did- cause problems. In fact, this had been the cause of what is now known as "the Decade of Ministerial Instability" under George II in the previous century. HM government have an interesting article of the development of the institution of Prime Minister on their website.
Finally, we should remember that political parties in the UK only began to coalesce into the kind of parties that we would recognise today in the late eighteenth / early nineteenth centuries, over the period from about 1760 to 1834. Previously, the "Whig" and "Tory" groups in Parliament are best thought of a loose coalitions of MPs with broadly similar views and goals. However, there was no "party line" on particular bills that came before Parliament. By 1834, the groups had become sufficiently well established that Robert Peel could issue the Tamworth Manifesto defining the goals of a "Conservative Party".
The split was effectively complete by the watershed election of 1852, where the two-party system of Conservative and Liberal parties emerged.
So, to answer your specific questions:
Normally the Prime Minister asked the monarch for a dissolution of Parliament. This could be because they could not command the confidence of Parliament or form a stable government (e.g. in the election of 1807).
Before the emergence of the two-party system in the middle of the century, contentious legislation on issues like Catholic emancipation or Parliamentary reform simply caused the various political coalitions to shift and reform. A Prime Minister on the "wrong" side of such legislation could easily lose the confidence of Parliament (or of the monarch who had appointed him).
Contentious legislation after the new parties had begun to emerge in the 1830s, such as that for the repeal of the Corn Laws, could split the newly formed parties and either strengthen the position of the Prime Minister (as was the case with Robert Peel in the election of 1841), or fatally undermine it (Robert Peel resigned in 1847, rather than asking for a dissolution of Parliament, fearing that the forthcoming election would become a vote of confidence).
Prime Ministers could also ask for a dissolution of Parliament because they sought to obtain a political advantage. This was the case in the election of 1806. Then, as now, such attempts to gain political advantage at an election were not always successful. Another general election followed in 1807!
As mentioned above, a dissolution would be triggered by the death of the monarch (e.g. the election of 1820).
In addition, in the eighteenth and nineteenth centuries it was normal for Prime Ministers to call for a dissolution of Parliament following an Act of Parliament that resulted in significant changes to the electoral system. This happened, for example, in the 1832 election following the Reform Act of 1832. However, when such an act came late in the life of the Parliament, as with the Representation of the People Act 1884, the election might be delayed, as happened with (the 1885 election).
The Prime Minister could ask the monarch for a dissolution of Parliament. Then, as now, meetings between the monarch and their Prime Minister are private, so we do not know how often, if ever, the Prime Minister's request was refused.
Parliament was able to make the Prime Minister's position untenable. In such cases the Prime Minister could either resign or ask the monarch to dissolve Parliament and force an election.
By the nineteenth century, the monarch no longer had the authority to dissolve Parliament unless asked to do so by Parliament itself, normally in the person of the Prime Minister.
The electorate had no say in the matter.
Click on the "election" link in the Wikipedia list of UK Parliaments for more details about each election.
Upvote:1
A British Parliament could last no more than seven years (until 1911 when it was changed to five), and as a practical matter, elections were often called in the sixth year. So I will focus on elections that either were called long before the sixth year, or involved a change of party. Here is a list of British general elections.
The key issue was the personalities that shaped these external events.
The first election of the 19th century, in 1802, was held "on schedule," six years after 1796. But in the next election, 1806 a Tory government in power that fell when its great anti-Napoleonic leader, William Pitt the Younger died. Its replacement, a Whig government lasted only one year, to 1807, being replaced by the Tories.
Other Tory governments fell at the deaths of King George III in 1820 and King George IV in 1830, respectively. The two Whig governments that followed were short-lived.
Beginning in 1835,the next few governments revolved around Sir Robert Peel. Technically a conservative, he was a "fusionist" who won a term in 1835. as a Whig-backed conservative Prime Minister. He also supported the Whig government that followed in 1837. and "defected" back to the Tories in 1841.
The Election of 1852 was considered a "watershed" election insofar as it decisively split Conservatives and Liberals into the Tory and Whig parties. (A similar thing happened in the U.S. in 1980 that pushed most conservatives into the Republican party and most liberals into the Democratic party.) The Tories became the Conservative party and the Whigs the Liberal Party.
Beginning in 1857, the mid-century elections were dominated by Lord Palmerston, who was a successful foreign policy manager. It was "accidental" that he was also a liberal, and therefore a Whig, but the election of this man on the back of foreign policy successes allowed the passage of liberal social reforms, especially after the crimean and Second Opium Wars of the mid-1850s.
In the latter part of the 19th century, the two leading Conservative and Liberal Prime Ministers, Disraeli and Gladstone polled nearly equally, but neither had a majority. Their governments were tossed about by splinter third parties, notably the Irish National Party, that held the balance of power.
Upvote:4
The key internal concerns were:
Main external concerns were Crimean War (1854) (their Great Game) and colonial Boer Wars.
In sum, the 19th century was a period of reform that gradually increased political democracy and improved economic and social conditions for the general population.
These improvements did not happen by chance.
To make such reforms happen, 19th century Britain had distinctive individuals who were willing to change (politically) or had a better way (of life, doing things, trade, etc.).
Key political leaders:
Individuals known for their ideas / political pressure:
Upvote:6
Parliament's key power then (and now) was to control the supply - i.e., the amount of money raised from taxation that went to the Crown. If the Crown (i.e., the government) could not get Parliament to grant the supply it sought then, in extremis, it had little choice but to dissolve Parliament and call an election.
Beyond that the Septennial Act of 1715 required that the Crown called an election at least every seven years (this was lowered to five years in 1911).
It increased the maximum length of a parliament (and hence the maximum period between general elections) from three years to seven. This seven-year ceiling remained in law from 1716 until 1911.
The Act overturned the provisions of the Triennial Act 1694, which "required parliament to meet annually and to hold general elections once every three years."