Opposition parties often submit amendments to bills, but it seems like they usually fail since the government uses its majority to vote against them.
How often do opposition amendments succeed?
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Opposition amendments very rarely pass when the governing party holds a majority in the House of Commons. In the last twenty years, no majority government has been defeated by an amendment tabled by the opposition in the House of Commons. The only defeats have been by rebel amendments tabled by backbench rebels from the party in government supported by the opposition - for example, the Cameron/Clegg coalition government's defeat on an amendment to the EU Multiannual Financial Framework in October 2012. On two occasions, opposition amendments passed in the House of Lords have been upheld in the Commons - these came under the Blair government in 2006 on two amendments to the Racial and Religious Hatred Bill.
The last time that an opposition amendment was successful against a government holding a majority in the Commons was in March 1993, when an amendment to the European Communities (Amendment) Bill - which implemented the Maastricht Treaty - proposed by Labour MP Dr. John Cunningham was passed.
Against governments with a minority, though, opposition amendments pass far more frequently. During the period between 2017 and 2019 when first Theresa May and later Boris Johnson governed, many opposition amendments passed - mostly on issues relating to the UK's withdrawal from the European Union, as well as a defeat on the Finance Bill in 2019; the first time a government had been defeated on a Finance Bill in over forty years. In one defeat in September 2019, the government simply didn't provide tellers for the No lobby, meaning an amendment proposed by Labour's Stephen Kinnock passed without a vote (see this related question).
A contributing factor to this is because amendments proposed by the opposition or passed in the House of Lords with sufficient cross-party support to succeed in the Commons are often handled by the government with a compromise amendment, known as an amendment in lieu when referring to a Lords amendment, in order to head off a backbench rebellion.
For example, the Johnson government was recently defeated in the House of Lords on two amendments to the Trade Bill, which sought to prevent the government from entering into trade deals with countries found by the High Court to be committing genocide. When the bill returned to the Commons, the government proposed an amendment in lieu, which included this provision, but instead gave the decision on pursuing such deals to Parliament. The Lords amendments were narrowly defeated, and the government amendment passed.