(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 1.7%, FTSE 250 adds 1.3% Jan 4 (Reuters) - British shares jumped on Monday in the first trading session of the new year as optimism around vaccine rollouts and a jump in oil prices helped boost the export-heavy index after it breached multi-year lows in the previous year. Ladbrokes owner Entain surged 26.2% to be the top gainer on the FTSE 100 after saying it received proposals from U.S. casino operator MGM Resorts for a possible offer. The blue-chip FTSE 100 rose 1.7% on its first day of trading with Britain outside the European Union’s orbit. The mid-cap index jumped 1.3%. However, limiting gains was Prime Minister Boris Johnson’s announcement on Sunday that tougher lockdown restrictions were probably on the way as COVID-19 cases keep rising. Plumbing parts distributor Ferguson Plc gained 0.2% after it agreed to sell its UK-focused business to private investment firm Clayton, Dubilier & Rice for about 308 million pounds ($421.56 million). Drugmaker AstraZeneca jumped 1.3% after Britain was set to roll out its low-cost and easily transportable COVID-19 vaccine, the second vaccine candidate to be distributed.