(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window) * FTSE 100 up 0.4%, FTSE 250 adds 0.2% July 29 (Reuters) - London’s FTSE 100 gained on Thursday, as encouraging earnings and huge dividend payouts from some of UK’s biggest corporates outweighed worries around rising inflation and COVID-19 cases. The blue-chip index rose 0.4%, led by oil major Royal Dutch Shell, miner Anglo American, and pest control company Rentokil Initial. Shell jumped 3.3% to be the top boost to the FTSE 100. Its second-quarter profit jumped to $5.5 billion, the highest in over two years, prompting the company to raise its dividend and launch a $2 million share buyback programme. Global miner Anglo American gained 3.6% after it increased its shareholder payout to $4.1 billion, including a $1 billion buyback, after bumper profits from the first six months of 2021. The domestically focussed mid-cap index climbed 0.2%. Lloyd’s Banking Group, caterer Compass Group and information provider Relx added 1.0% to 2.5% after reporting strong results. (Reporting by Shashank Nayar in Bengaluru; editing by Uttaresh.V) Our Standards: The Thomson Reuters Trust Principles.