Wow, that is weird! I'm so used to making sure I have my ID with me all the time. But what will I need it for? I'm not going to have a car and I guess bartenders aren't as strict about carding folks over there to buy alcohol as they are here. (I'm 32 and still get carded over here sometimes.)
You don't have to carry ID with you in the UK, as it's not often you will need it... and when you do need it, you will normally have ample warning of it so you can bring your passport or other ID with you (i.e. if you have a job interview or an appointment with the bank or something, or even if you know you're going on a night out and might get carded).
Sometimes it can be useful to have ID with you though, as retailers take part in the the 'Challenge 25' scheme, where they can ID you for alcohol if you look under 25. I'm almost 31 and I get carded for alcohol in the UK every single time I buy it (possibly because apparently I still look about 16 :S)... in fact I think the last time I
wasn't carded was when I was only 17 and not even legally allowed to buy it yet

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However, most people use their driving licences for ID here, rather than a passport or ID card. Even if you don't drive, you can apply for a provisional UK driving licence when you arrive (which you need in order to take the UK driving tests and get a full licence), and then you can just use it as ID instead.