The Local has a section dedicated to Brexit, and specifically how Brits in Sweden will be affected by the various possible outcomes. You can follow Sweden-related Brexit news here, or if you're interested in more general Brexit updates, including those focused on other parts of Europe, you'll find The Local's pan-European Brexit coverage here.
This is where you need to go for information from the government on how Brits will be affected, including any new permit requirements or law proposals. Initially this section was only available in Swedish, but since February it's been possible to read the main Brexit updates from the Swedish government in English. Of particular importance to Brits in Sweden is the page detailing the likely effects of Brexit on “the citizens who are particularly affected” and the advice provided for those who run businesses in Sweden.
The Swedish Migration Agency (Migrationsverket) also has a page dedicated to Brexit. At the moment, while the outcome of the negotiations is still unknown, it's extremely sparse, but once a deal has been decided or the UK leaves the EU, this is where you'll find information on what permits will be needed post-Brexit and how to apply. There's more information on the Swedish-language version of the page, though.
If the UK leaves without a deal, Sweden has granted a one-year 'grace period' allowing Brits to stay in Sweden while retaining their current rights and giving them time to apply for permits. Brits will also be able to apply for a proof of this status (in the form of a passport stamp) and it will be possible to do that online via the Migration Agency's website if a no-deal Brexit is confirmed.
This is particularly useful for those working in the tech industry, but could also provide insight for others. There's a 'checklist' of questions you should be asking yourself if you run a business in Sweden, from how staff could be affected to how to potential delays of imports and exports at the border, and it's available in English too.
This website focuses on the economic and commercial consequences of Brexit, which will be useful mainly to those working as sole traders or business-owners in Sweden. There's analysis of the possible consequences, including relating to the free movement of people.
Again, as the name suggests this information is targeted towards those in the business sphere. Here it's even possible to sign up for a course on preparing your company for Brexit, and there's plenty of English-language information on trading with non-EU countries.
The British Embassy doesn't have an individual website, but it's well worth following the British Embassy in Stockholm on Facebook to keep on track of any announcements, and to ask your questions. This is also where you'll find out about events such as town hall meetings held across the country to hear the latest updates from officials in person (recently they've live-streamed some of these events on the Facebook page too).
Citizens' groups on Facebook
In Sweden, the main Facebook group aimed at British citizens is British in Sweden, part of the EU-wide British in Europe group, which also has its own website. You may also want to look at other EU-wide groups for Brits living in the EU, such as Expats in Europe After Brexit and Brexpats – Hear Our Voice, or the many Facebook groups for Brits and other international citizens in Sweden, for example The Local's own Living in Sweden group or Expatriates in Sweden.