#1 - ABSOLUTELY. Having recently moved in London, my first approach was to search sites like RightMove, etc. and create a little spreadsheet of 15 properties we'd shortlisted. After calling each estate agent, not a single property was actually available. Incredibly frustrating.
edit: Also regarding charges, parking data (whether it's included, or if not how much is an on-street permit from the council, etc.) would be great!