(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 0.2%, FTSE 250 adds 0.1% June 22 (Reuters) - British shares rose on Tuesday as investors hoped that the central bank will keep interest rates at record lows despite a recent rise in inflation, while heavyweight energy shares tracked a jump in oil prices. The benchmark FTSE 100 index climbed 0.2%, with Melrose being the top gainer on its plans to return about 730 million pounds ($1.01 billion) in cash to its shareholders. The energy index was among the top gainers, rising 2.03%. The domestically focussed mid-cap index rose 0.1% British public borrowing fell in May from sky-high levels of a year earlier when the government was ramping up a huge spending response to the coronavirus crisis, and there are signs that the recent recovery in the economy was boosting tax revenues. GlaxoSmithKline fell 0.5% ahead of plans to boost the spending power of its research-focused pharmaceuticals business at an investor day on Wednesday, as analysts call on the British drugmaker to boost drug development prospects with takeovers or alliances. Reporting by Shashank Nayar in Bengaluru; editing by Uttaresh.V Our Standards: The Thomson Reuters Trust Principles.