Lloyd's of London Insurance
There is no proper term to use when requesting "bank deposit insurance", but the insurance company (i.e. Lloyd's of London) should protect against the bank going insolvent or a bank run creating a liquidation issue for one's deposits.
NOTE: Lloyd's of London does not have a single contact point, as they are a group performing underwriting. One will need to reach out to their contacts in either the UK enquiries@biba.org.uk or individual insurance buyers within the USA can find independent insurance agents through the IIAA at
www.trustedchoice.com