There were rules that applied during the transitional period, and rules for after that period was concluded.
During the transitional period
A transitional period was put in place until 31 December 2020. During this time, British citizens and their family members continued for the most part to have the same rights as they had before. Among other things, this meant that they were exempt from paying application and tuition fees for higher education studies in Sweden.
After the transitional period
The transitional period expired on 31 December 2020. Currently, British citizens and their family members designated in article 10 of the Withdrawal Agreement - those who exercised their right to reside in Sweden before the end of the transitional period, and continue to do so - are not required to pay application and tuition fees.
British citizens not covered by the Withdrawal Agreement - or any other fee exemptions - are required to pay both application and tuition fees starting 1 January 2021.