Will Fitzgerald has asked me more than once to cover British use of the adjective sorted. It has made an appearance on the blog before, as part of an Untranslatable October. But that short bit on it does not really give it its due. In the Corpus of Global Web-Based English, the word sorted is found more than three times more frequently in British than in American English. It's definitely a word to know if you interact with British people.

The OED has three UK-particular meanings for it in their 2001 draft additions. I'm going to cheat share the fruits of their defining, with some fresh examples.

The first sense, and by far the most frequent one, is illustrated in a current British Transport Police campaign, with posters like that at the right.

 a. Chiefly Brit. slang. Of a state of affairs, etc.: fixed, settled, secure; arranged, prepared, dealt with. Chiefly used predicatively and (esp. in earlier use) frequently indistinguishable from the past participle of the passive verb (cf. sort v.¹ 16a(e)). Also as int., esp. used to express assent to a proposal, readiness to act, or to mark the satisfactory conclusion of a transaction.
This sense is perhaps influenced by a British Army slang use of the verb meaning ‘to attack fiercely, to shoot to pieces’

The implication of the "See it. Say it. Sorted." slogan is that if you report suspicious things you see, the police will take care of it. They will (BrE) get it sorted. In AmE and more usually (until recently) in BrE, you'd have to say that the police will get it sorted out. As the entry says, this probably comes from an older (1940s) Army usage, but this more modern sense seems to have got(ten) going in the 1980s. Here are a couple of recent examples from UK news websites, courtesy of the News on the Web corpus.

The EU’s 27 member states have insisted that talks cannot move onto trade and commerce until the three key issues of EU and British citizen residency rights, the UK’s so-called divorce bill and the border with Ireland are all sorted.  (Verdict)

Your entertainment for the rest of the year is sorted with our 2017 guide. (East Anglian Daily Times)

Another example, from the GloWBE corpus, is an interesting case of sorted before the noun it's modifying:

I would make it a nice outing with your son to a well sorted hifi shop where you actually have time to listen. (from a hifi discussion board)

The second meaning comes along in the early 90s (at the latest), and is used particularly of people.

 b. Brit. slang. Esp. of a person: self-assured, emotionally well-balanced; streetwise, ‘cool’.

This one may be a bit dated. I don't feel like I hear it as much as I used to. I'm certainly having trouble finding a clear example of it in the corpora. It's the kind of thing you might read in a (orig. AmE) personal ad. I'm not signing up for a singles site to research this for you, so here's a bit from the Yorkshire Post about the word:

Today, people are perhaps a little more transparent in the language they use to describe themselves in personal ads. But, just as "bohemian", "sporty" and "adventurous" in a woman and "artistic" in a man could be loaded with meaning a century ago, today's more mainstream lonely hearts ads can still require a full glossary of euphemisms, from "sorted" (no weirdos, no baggage) to "creative" (possibly "willing to experiment" or simply "not boring").

You can see that kind of usage in one of the OED examples. 

1993   T. Hawkins Pepper xiv. 268   Thank you so much for replying. You seem really sorted.

The third OED sense is one I'm not sure I would have counted as separate from the first:

 c. Brit. slang. Of a person: supplied with or under the influence of illicit drugs, particularly those associated with the U.K. club subculture.

You sorted? is the kind of thing you'd expect a drug dealer to say. Here's the OED's first example for it:

1991   Independent 23 Dec. 5/2   Are you sorted? It's good stuff, it'll keep you going all night.

So that's sorted sorted. The first sense is the one you're most likely to run into.

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Apologies for no blog posts in August. I was very busy with getting the last changes to my book manuscript off to the publisher. Publication date is 10 April, but I'm going to wait to share moreinfo until both publishers (US and UK) are ready to take pre-orders. (It would not be good for my nice UK publisher if British folk were ordering from the US.)  I'm afraid that blogging will probably be sparse in the Autumn as I have my whole year's teaching load in one term. But one of the things I'm teaching is a new (BrE education jargon) module (=AmE course) called Language in the United States. Maybe that'll inspire some bloggy procrastination. Or maybe I'll get some guest posts from my students!

Today, people are perhaps a little more transparent in the language they use to describe themselves in personal ads. But, just as "bohemian", "sporty" and "adventurous" in a woman and "artistic" in a man could be loaded with meaning a century ago, today's more mainstream lonely hearts ads can still require a full glossary of euphemisms, from "sorted" (no weirdos, no baggage) to "creative" (possibly "willing to experiment" or simply "not boring").

Read more at: http://www.yorkshirepost.co.uk/news/analysis/strictly-personal-behind-the-lines-with-a-history-of-lonely-hearts-1-2334630