In the UK, there are some key differences. Our budgets are not about parliament authorising spending by government, they are just about how the government plans to tax us to contribute to the government spending.
The second key difference, in the UK we do not vote for our prime minister. We vote for a local MP, usually based on his party membership and the policies of that party. This means UK government MP’s are fairly closely aligned to our prime ministers policies. US politicians are elected seperately from the choice of president, often on a different time, and based on their own local platform.
Finally, in the UK, opposition parties will strongly oppose government legislation, if they think its a poor approach. However, in the House of Lords ( a bit like the US senate) there is a gentleman’s agreement to only amend, but not block laws that were part of an election promise.
In the UK, there have been occasions when budget announcements did not get the full support of parliament, but it would only prevent changes from occurring. Government carries on as before.