NO Appley Manor Hotel and others like you around the country – you DON’T have to insist that people give you their personal details

UK government website: 

If someone does not wish to share their details, or provides incorrect information

Although this is voluntary, please encourage customers and visitors to share their details in order to support NHS Test and Trace and advise them that this information will only be used where necessary to help stop the spread of COVID-19.

If a customer or visitor informs you that they do not want their details shared for the purposes of NHS Test and Trace, they can choose to opt out, and if they do so you should not share their information used for booking purposes with NHS Test and Trace.

The accuracy of the information provided will be the responsibility of the individual who provides it.

You do not have to verify an individual’s identity for NHS Test and Trace purposes.

https://www.gov.uk/guidance/maintaining-records-of-staff-customers-and-visitors-to-support-nhs-test-and-trace