How does the government leak things to the media

A good example would be the sort of leaks that are likely to happen before the October budget and that have happened similarly before financial announcements in the past. How high up is this likely to go? Does some senior civil servant at the Treasury decide or are they under orders from officials even higher up?

How does this work in general? Do the government try and hide from the media that it's them, and if so, what sort of method would they use to send the information?

A similar idea goes for political announcements. The US government (not confirmed but very likely) a while back leaked to the NYT a load of confidential documents about a ceasefire agreement being made more difficult by Netanyahu. I know this is about UK politics but the UK government would probably do something similar. Perhaps we might see this with a youth mobility deal before it is officially announced. But again who makes the call and how much effort does the government put in to hide that it's them?​