I can only talk from the US of A point of view.
Forgive me for saying this, but when you're in an ER, honesty is not the best policy. Here's why. If they decide you're dangerously suicidal, they'll put you in a hospital. The problem is that it could be any hospital. If you run out of luck and all the private hospitals are full, they'll put you in a state hospital (there must be an equivalent to this in the UK, I'd imagine), which will be misery and zero therapeutic value. It's a much better idea to commit yourself voluntarily, so you can pick and choose which hospital you want to stay in.
Now, based on the posts so far, it seems the UK may be more efficient and structured than the US's style, which I think is haphazard and astronomically inefficient. Here's how the US style works: You sit in a waiting room until you see a nurse. You describe your problem to them. You'll be waiting a while after that until you're escorted into the mental health unit. You'll be given somewhere to stay, usually a bay with a bed, and once again, they'll ask you to wait. But, bless their souls, they may give you something to help you relax (in my case, Ativan), which will literally make the experience feel downright pleasant. You'll then get your blood drawn and vitals taken, then you'll wait some more. At some point you'll be seen by a doctor, but he's not the important one. He'll ask you general questions about why you're there, but it's not him you want to win over. After him, you'll see the guy who evaluates you.
This is where it gets touchy. He'll ask you all kinds of questions, the most important being something along the lines of, "Do you feel like you are a danger to yourself or others?" Say yes, and you'll be given a hospital. Say no, and they'll test you some more. So, hypothetically, let's say you say no. You wait some more until another evaluator sees you--but this time, it's in a special area, surprisingly luxurious, and dead quiet. This guy will ask you almost identical questions as the guy before him, but I swear to God he was trained to make you answer yes to that question. He'll question you some more, a lot more, and wear you down. He knows you're dead tired, weary from hours of waiting, and broken-spirited. The interview is lengthy, and by now they'll have drugged you to make you more docile, and thus more truthful. And he'll ask you again, "Do you feel like you're a danger to yourself or others?" The same rules apply.
There aren't that many possible outcomes. Either you're hospitalized or sent home.
There is no such thing as a crisis team in the US. That's something unique internationally.
You really have to walk in determined to get one thing or the other. I was always sent involuntarily, except for once, but it was because I had a different purpose for being there on that one visit.