Before Brexit (until Jan 31, 2020): As EU citizens, Bulgarians and Romanians had full freedom of movement to live and work in the UK without a visa or work permit, subject to registration after three months and self-sufficiency requirements.
After Brexit: The UK now operates its own points-based immigration system. Bulgarian and Romanian citizens are no longer automatically entitled to work in the UK. They generally require a skilled worker visa (or other applicable visa) sponsored by a UK employer, meeting salary and skill thresholds.
For the latest rules, consult the UK Government's official immigration website.