Yes - the UK Government encourages you to do so - here are the relevant extracts from the official guidance as of November 12th, 2020.
"As testing technology becomes more widespread, we know that some employers may want to test asymptomatic employees in their workforce on a regular basis. We have therefore produced this practical guide to encourage them to do so."
"Important: NHS Test and Trace is for those who display symptoms of COVID-19 or who have been advised to take a test by a medical practitioner or public service. Employer and third-party healthcare providers wishing to provide a test to staff must not advise individuals without symptoms to get a test from the limited supply offered by Test and Trace, but may offer alternative private provision, in accordance with this guidance."
"The current NHS antibody testing service is targeted at NHS patients and staff, and social care staff and residents, and is not accessible by private employers."
"It is a voluntary decision for employers to run testing programmes for their staff. If done correctly, testing can provide confidence to employees and customers in the workplace and may help to protect business continuity."
"Where employers are considering – or are already running testing programmes – this guidance sets out the legal obligations and best practice to follow, ensuring new and innovative programmes are as reliable and effective as possible."
"All employers and employees must follow the guidance for employers and businesses on coronavirus (COVID-19)on COVID-19 protective measures in the workplace, regardless of the result of either a virus or antibody test."