The British Library collects company annual reports through legal deposit. They have good historical coverage for some companies but the holdings are not complete for all companies. The reports are not on the British Library's catalogue. The reports can be viewed in the Business & IP Centre. The Business & IP Centre also has databases that provide facsimile copies of reports.
Fame includes annual reports for UK and Irish companies. Search for a company, click on 'Original documents' and look for 'Annual Accounts'.