The House of Lords is a vestige political body with only powers to delay legislation, but because it is unelected (as of yet), it actually serves a very useful function in British politics.
Montesquieu, whose political theories heavily influenced America's founding fathers (especially regarding the balances of powers in government, which he greatly admired in the British government at the time), also supported hereditary aristocracy. In any case, most of the House of Lords are not longer hereditary peers, as life peers are now the norm.
The reason an aristocracy is *sometimes* desirable in government is that they do not have to answer to the whims of the masses as they are not elected. The political fervour that is whipped up in the populace, from security theatre / war on terror, the war on drugs, etc, takes a life of its own in a pure democracy. The idea is that you with an aristocracy, the actors can take a long term view and can judge and react independent of popular sentiment.
The British parliamentary system actually contains elements of three different types of government - Monarchy (constitutional, providing the head of state which is apolitical), aristocracy (the House of Lords comprises of hereditary peers and also life peers appointed for certain accomplishments), and democracy (the House of Commons). The House of Commons, as the constitution currently stands, holds all of the cards, but the House of Lords (and to a lesser extent, the Crown) also serves to temper the populist nature of the politics in the House of Commons.
As the government is formed by the biggest party in the Commons, the executive is formed by the biggest party in the legislature, it is no surprise that the British system is more productive politically - it rarely ends in gridlock like the US government. If it does (the government losing confidence of the Parliament), then new elections are called to end the gridlock. Arguably, if America adopted this system, it would be a huge step forward. This also points to a major advantage of a system with a unwritten constitution - the political system can gradually evolve, whereas in countries with written constitutions (such as the US), it is much more difficult for better or for worse.