I think you will find you need to display on the premises your certificates of insurance.

Google said yes

https://www.gov.uk/employers-liability-insurance#:~:text=You%20can%20be%20fined%20%C2%A3,to%20inspectors%20when%20they%20ask.

Employers' Liability (Compulsory Insurance) Act 1969: A brief guide for workers HSE39

Since 1 October 2008, employers have been allowed to satisfy this requirement by displaying the certificate electronically. If your employer chooses this method, they must ensure that you know how and where to find the certificate and you have reasonable access to it.

But its still the certificate - not a letter.

.Also remember public liability insurance is not compulsory - but you have to be a bit silly not to have it

Generally one of the first things I am looking for when attending a new site, supplier or customer.

Typically found on the reception (or gatehouse clocking point) notice board along with the ISO certificates all capable of being out of date and a good indicator if people are maintaining workplace communications in a timely manner.

The comment about electronically is fine for organisations where everyone has access via a computer they are permitted to use during working hours - not all employees do.