(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 0.5%, FTSE 250 adds 0.3% Jan 21 (Reuters) - British shares tracked gains in Asian peers on Thursday, lifted by hopes of a swifter economic rebound this year and more U.S. stimulus, while Pets at Home headed higher after reporting upbeat quarterly results. The blue-chip FTSE 100 index gained 0.5% by 0804 GMT, while Asian shares hit a record high. The domestically focussed FTSE 250 index added 0.3%, with industrial stocks leading the gains. Bank of England Governor Andrew Bailey said he expected Britain’s economy to recover strongly as the country moves ahead with vaccinating its population against COVID-19. Pets at Home Group Plc rose 0.4% after reporting an 18% jump in third-quarter revenue, helped by higher demand for its accessories and veterinary services. Sports betting and gaming company Entain Plc climbed 0.9% after naming non-executive director Jette Nygaard-Andersen as its top boss, making her the first woman to lead a company in the UK gambling industry. Trading platform IG Group fell 1.6% after it said it planned to buy online brokerage tastytrade for $1 billion, as it ramps up its presence in the United States after a stellar year for the industry. (Reporting by Shivani Kumaresan in Bengaluru; editing by Uttaresh.V)