So in practice, the PM of a majority gov't (i.e., has a majority of seats) gets to pass whatever they want to pass; the saving grace of this is that, without having to haggle and herd cats and trade horses, the legislation is the legislation--there's no poison pills, no payoff amendments, no loopholes to capture one person's support, and no extreme bits to trade away. It's just "this is the law we want", which I think leads to higher quality legislation over all.
The PM of a minority gov't (i.e., only has a plurality of seats) may have to secure another party's vote to pass, but that's a negotiation with a second entity, not a hundred other voting entities.
Consensus doesn't play a significant part in it, I believe. Within the bounds of the law, the PM of a majority is nearly a polite dictator.
In a parliament majority, the buck stops with the Prime Minister and win or lose his performance is on the line in the next election. There's no (effective) hand-waving about opposition or other excuses to deflect accountability. Elections are a black/white referendum of the incumbent's performance.
In the US it's a lot easier to muddy the waters and a lot harder for people to arrive at a clear conclusion and often nobody is happy.
"YES I don't like X BUT it wasn't Y's fault it was Z"
No, I'm not. The concept of a party whip literally invented where I'm from. I'm very much familiar with it.
The US system is much more adversarial. Even if a single party gets the house, senate and presidency, there isn't much stopping individual party members from voting against the party line.
It's true consensus is need with a coalition/minority government, but they don't seem to happen that often. Yes, I know there is one right now.
Proportional representation is almost a necessary condition for the parliamentary system to encourage consensus-building. More specifically, it's necessary that no party hold an absolute majority.
With first-past-the-post, you usually end up with one party having full control for one term, and no one to hold them accountable (particularly if you have the principle of parliamentary soverignity).
With some of the NI parties screwing over conservative governments its why NI doesn't have the same laws as the UK
[Aside: An interesting consequence of this is that England lacks a legal and political identity separate from the UK as the UK is an _extension_ of the Kingdom of England. Another interesting this is that even though it was part of the Kingdom of England, Wales _does_ have a legal and political identity because there are acts of parliament that _explicitly_ refer to it. The UK is a constitutionally odd country.]