Lloyds, in its insurance period, was really a co-working space. That approach to insurance required multiple people to assume part of the risk. Each insurer would sign their name on a contract, below other names. This is where the term "underwriting" comes from. They had to get together somewhere to do this.

It's probably not authentic, but you can see the Hollywood version of Lloyds Coffee House in "Lloyds of London" (1936)[1], around 25:30.

[1] https://archive.org/details/1936LloydsOfLondon