Yes and without permission if they have indefinite leave to remain in the UK (aka settlement or permanent residency).
EU citizens were able to apply for settled status or pre-settled status (depending on whether they had under or over 5 years’ residency in the UK already at 31 December 2020) under the EU Settlement Scheme. The deadline for applications was 30 June 2021.
Some citizens can view their immigration status online and provide a share code to prove their status to employers.
Otherwise there is a new points-based immigration system. EU citizens will need to be sponsored ordinarily by an employer before they can apply to enter the UK and work. There are various routes – such as the Skilled Worker route.
There are some unsponsored business-related routes too (such as a business visitor).