(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window) * FTSE 100 down 0.5%, FTSE 250 down 0.3% Feb 17 (Reuters) - London’s FTSE 100 fell on Wednesday as inflation picked up by a little more than expected in January, while British American Tobacco slumped despite stronger annual profit. The commodity-heavy FTSE 100 was down 0.5% by 0819 GMT, with British American Tobacco the biggest drag. British inflation rose a little more than expected last month as the country went back into a coronavirus lockdown, pushed up by higher food prices and less discounting of household goods such as sofas, official data showed The mid-cap FTSE 250 index fell 0.3%. British fund supermarket Hargreaves Lansdown slid 7.6% to the bottom of the blue-chip index after Peter Hargreaves, the largest shareholder and co-founder, sold $416 million worth of shares. (Reporting by Shivani Kumaresan in Bengaluru; Editing by Sriraj Kalluvila)