New government regulations came into effect at midnight on Sunday 27th September, which set out mandatory periods for self-isolation.
The Health Protection (Coronavirus, Restrictions) (Self-Isolation) (England) Regulations 2020 include an obligation to notify the Secretary of State of the names of all those in the same household as someone who has tested positive for Covid-19.
Of note is the fact that it is now an offence for an employer to knowingly permit a worker (including an agency worker) to attend a place of employment when they should be self-isolating. This covers those in the same household as someone who has had a positive test and is therefore required to self-isolate.
The onus is therefore on the employer to stop someone from working if they should be self-isolating under the regulations. Fines for failing to do so start at £1,000.
Workers are also required to inform their employer if they are self-isolating. Failure to do so is a criminal offence.
You can read the regulations in full here