People from EU countries, including Slovaks, living, working and studying in Great Britain prior to Brexit will not have to leave the country, as reported by the TASR newswire.

However, they are obliged to apply to the EU Settlement Scheme, which is now open and free. The deadline is June 30, 2021. But if Britain leaves without a deal, the deadline is sooner - December 31, 2020.
The UK is to leave the EU on October 31, 2019 or as soon as the Brexit Deal gets approved at Westminster.
Successful application
To apply to the scheme, EU citizens will need a valid passport or national identity card and a digital photo of themselves. They will also be asked to submit their criminal records issued by the UK or overseas.