During that time, British citizens would be able to continue living and working in Sweden without a residence or work permit, thereby giving them time to apply for the relevant permissions.
"The Migration Agency welcomes this pragmatic solution," the note stated, but added that the exemption from residence and work permit requirements would be a temporary measure.
In other words, British citizens would almost certainly need to apply for permits in order to continue living in Sweden after the one-year period. The agency called on the government to aim for a "resource-efficient solution", to keep the agency's workload to a minimum and to keep things simple for affected individuals.
The cost of processing the necessary permits for British citizens was estimated at 62 million kronor ($6.7 million), even taking into account the increasing number of Brits who are in the process of applying for Swedish citizenship. In total, around 2,500 Brits are expected to be granted citizenship by the end of 2019, and this group would therefore not need to apply for a permit.
One issue noted in the statement is that there is no record of the reason Brits in Sweden have for moving to the country. Since May 2014, it has not been necessary or even possible for EEA citizens to register their right of residence with the agency.
The agency estimated that more than half of the estimated 20,000 British citizens in Sweden were in the country primarily for work, while 15-25 percent had moved in order to live with a partner, and a further 10-15 percent were students.
"The majority of the British citizens [in Sweden] work in highly qualified professions and their cases are not considered to require such thorough investigation," the agency said.
The agency also noted that it is possible that some Brits could be denied right of residence after Brexit, if the government decides that the existing rules for third-country citizens will apply, and it called on the government to make a decision "quickly" on what framework would be used for Brits.
"It is also important that it be made clear as soon as possible whether any special legislation simply means that British citizens and their family members can apply [for a permit] from within the country, or whether there will also be special rules granting British citizens and their citizens permits," the message noted.
During the 'year of respite' starting on March 29th, 2019, the government has proposed that Brits be able to apply for a written proof of their status in Sweden, allowing them to travel, for example. But this would not apply to family members of Brits who are citizens of another non-EU country, making it hard for this group to travel for work or with their family.
FOR MEMBERS: How to get citizenship as a Brit in Sweden
Photo: Pontus Lundahl/SCANPIX/TT
What's more, the agency said that the ongoing uncertainty about the process meant it "could not be ruled out" that they would not be able to process all the necessary permits by March 2020, which could cause problems for the Brits who had not received a permit by that time.
The government proposed that these decisions would be made by applying online, but the Migration Agency said: "Given the very short timeframe which is available for Brexit-related judgments, Migrationsverket's assessment is that there is no scope for any form of digitalization of judgments relating to British citizens."
And it further warned that the situation could lead to "legal questions and possible complications which are hard to predict today".
The impact of a no-deal Brexit is likely to have an impact on other foreign nationals in Sweden too. "Other judgments will need to be de-prioritized in favour of British citizens and their family members, and processing times for other judgments will become longer," the agency warned.
The government's proposal would only come into effect if the UK leaves the EU without reaching a deal beforehand.
In a previously agreed withdrawal agreement, which has since been rejected by the British parliament, UK and EU negotiators agreed to a two-year transition period during which British citizens could continue to move to EU countries, and vice versa, without needing a permit.
Under that agreement, Brits already living in Sweden, as well as those who move there before the end of the transition period on December 30th, 2020, would retain many of their current rights for the rest of their lives. However, this deal was voted down by British MPs in January this year, and no alternative agreement has yet been reached.
READ ALSO: How Brits in Sweden are (and aren't) preparing for Brexit