Pam, i have had this reply from leicester library:
With reference to your enquiry about William Moss and Lloyd's bank: there is some information in our resources about the building, but no mention of the construction company - details below.
1. Taylor, Michael. The quality of Leicester. Leicester City Council, 1993.This book contains a short description of the building on p135, referring to the design by Chatwin and Son of Birmingham.
2. Community History Newsletter Issue 53, Summer 2006. Published by Community History (part of Leicester Libraries). This issue features quite a detailed (3 pages) article about the building by Graham Hulme, entitled "From banqueting house to banking hall" - but does not mention the construction company.
3. Wrights Directory of Leicestershire and Rutland 1900 lists a W. Moss and Son, Builders and Contractors, at 39 Baxter gate in Loughborough.
All of the above are available for reference at the Learning and Information Library in Bishop Street, Leicester.
Two other potential sources of information are:
Loughborough Library - which has an extensive local history collection.
Leicestershire Records Office - opening hours and contact details are on their website:
http://www.leics.gov.uk/index/community/recordoffice.htm Diddy