In the British Parliament, the party that governs is, by convention, the one that can command majority support in the House of Commons. Once that majority is secured, the government is entitled to propose whatever legislation it wishes. In the United Kingdom, Parliament is sovereign and there exists no other institution with the power to strike down legislation in the same way as the US Supreme Court. The British constitution is unwritten, and so there is no mechanism by which judicial review may be used to void Acts of Parliament. English courts can certainly rule government actions unlawful, but it cannot strike down legislation.
Both houses of Congress are wholly elected. In the United Kingdom, however, this only applies to the lower house, the House of Commons. The unelected House of Lords—the upper chamber in the UK Parliament—can certainly delay legislation and inflict defeats on the government of the day. However, if needs be, the government can always enforce the Parliament Acts, which ensure that the will of the democratically-elected House of Commons will eventually prevail.
Unlike the United States, there is no separation of powers in the British system of government. All members of the government are either members of parliament (MPs) or members of the House of Lords. In the United States, the executive is strictly separated from the legislature, and so senators and members of Congress cannot serve in the executive branch and vice versa.
The role of the monarch is arguably the greatest difference between the two systems. However, that role is purely formal; the monarch reigns but does not rule. All Acts of Parliament must be given the Royal Assent before becoming law. But this is a mere formality and is never refused. Nevertheless, it's a notable feature of the British system that the government of the day is known as Her Majesty's Government (or His Majesty's Government when there's a king on the throne), and members of that government are known as Ministers of the Crown. This provides another example of overlap between the executive and the legislature in the British constitution.