Go to FTSE UK Indices: Select Constituents of the index you want.
Use Datastream available at Barcelona and Madrid Libraries (through LSEG Workspace). Select category Constituent Lists, search for the index you require and do a static request for company name. Easier using the Datastream Advance for Office Excel Add-In.
Constituent information is also available from the London Stock Exchange Indices webpages. However, this is not in a form that makes downloading the complete list easy.