In accordance with the EU law, UK citizens are entitled to stay and work freely in the Czech Republic without any permits being required (e.g. visa, work permits etc.)
The situation, however, is to change with the withdrawal of the United Kingdom from the European Union on 29 March 2019. The legal status of UK citizen has not still been cemented since the negotiations over the specific withdrawal arrangements agreement, which would also address the above issue, have not finished so far.
As matters stand at the moment, the current agreement proposal suggests that the rights of UK citizens living in another EU member state be retained till the end of 2020. Due to the continuing talks it is impossible to positively say whether the above rule will be included in the withdrawal arrangement or not.
If not, UK citizens will need either visa or stay permit to prolong their stay in the Czech Republic; the specific procedure and further details are still a matter of speculations.
Otherwise, the UK citizens will have an opportunity to prove to the Czech Ministry of Interior that they have stayed in the Czech Republic before the Brexit and, hence, they will enjoy their rights (such as a right to stay, access to the job market etc.) till the end of 2020. The Czech Ministry of Interior has issued a warning that such procedure may be a fairly difficult one. Nevertheless, there is yet another, much easier way – obtaining a so-called certificate of temporary residence before the Brexit will suffice; according to the Ministry, the document conclusively proves that “its holder is an UK citizen who stayed in the Czech Republic before the date of the withdrawal of the United Kingdom from the European Union”.
To issue the certificate, the applicant needs to present basic documents related to their stay in the Czech Republic to the Ministry, and the certificate is issued free of charge. The UK citizens are recommended to follow the procedure, not only because of matters of legal uncertainty regarding their status in the Czech Republic, but also for the reasons of time saving and avoidance of onerous proceedings with competent immigration authorities.