There is guidance on Gas Safe and HSE about safety inspections for vulnerable shielding etc.
If you don't want them in then you should be prepared to put in writing:
CORONAVIRUS (COVID-19): ADVICE FOR LANDLORDS
The HSE have provided the following guidance for landlords.
Landlords have a duty of care to their tenants. This is a legal duty to repair and maintain gas pipework, flues and appliances in a safe condition, to ensure an annual gas safety check on each appliance and flue, and to keep a record of each safety check. During the Coronavirus (COVID-19) outbreak, there is a balance between ensuring people, including the vulnerable, are protected from possibly fatal risks arising from carbon monoxide exposure or gas explosion, while doing what we can to protect people from COVID-19.
Current guidance from HM Government states that work can still be carried out in people’s homes where necessary, eg for reasons of safety, provided that the GOV.UK guidance on social distancing is followed. See ‘Advice for engineers’ for guidance for engineers and their employers regarding working in peoples’ homes.
The law is flexible and where it is not possible to carry out a gas safety check, it will normally be enough to show that you took reasonable steps to do so. In the event you are unable to gain access to the property, eg refusal of access due to tenants self-isolating, or if you are unable to engage a registered gas engineer to carry out the work due to a shortage of available engineers, you will be expected to be able to demonstrate that you took reasonable steps to comply with the law. This should include records of communication with the tenant and details of your engineers attempts to gain access. You should seek to arrange the safety check as soon as all parties are available.
Landlords should not suspend all gas safety checks at this time as it will unnecessarily put tenants at increased risk, particularly as people are spending most, and in some cases all, of their time at home. Each property should be considered on a case-by-case basis, completing safety checks where tenants permit access and gas engineers are available. If you are unable to secure the services of your usual engineers, you must make reasonable attempts to obtain alternative services. Where you cannot and resource has to be prioritised you can do so, taking into account factors such as (this list is not exhaustive):
the age and type of appliances;
previous maintenance/work carried out;
breakdown history;
the presence of CO alarms; and
whether the tenant is considered vulnerable for reasons other than risk from coronavirus (COVID-19).
Example scenarios
These example scenarios are to help landlords understand what may be considered reasonable steps to take, to demonstrate compliance with their duties to have appliances checked annually (under the Gas Safety (Installation and Use) Regulations) during the coronavirus (COVID-19) outbreak. They are not exhaustive. Landlords will need to assess the risks for each situation on a case-by-case basis.
See also Ministry of Housing, Communities and Local Government Coronavirus (COVID-19) Guidance for Landlords and Tenants.
Scenario 1 – Vulnerable person
Example: Your tenant informs you that they do not want anyone to come to their home as they fall into the Government’s vulnerable people category (they are aged 70 or over and/or are at increased risk of severe illness from coronavirus).
What you must do: You can delay completing the landlords gas safety check until after your tenant’s isolation period has ended. You must arrange for this to take place as soon as possible after the isolation period has ended.
You must be able demonstrate that you have taken reasonable steps to arrange and reschedule the gas safety check; we strongly advise that you keep records of all communication and correspondence with the tenant, including emails and text messages if applicable.