Oct 5 (Reuters) - London"s FTSE 100 rallied from recent losses on Tuesday as signs of a recovery saw investors piling into economically sensitive sectors, with energy stocks rising as oil prices hit three-year highs. The blue-chip FTSE 100 index (.FTSE) gained 0.9% after three straight sessions of losses, aided by over 2% jump in both banks (.FTNMX301010) and life insurance (.FTNMX303010) stocks. The benchmark UK 10-year bond yield touched a more than two-year high on persisting inflation expectation and bets on rate hikes by central bank. "I think today is a continuing trade. Since we"ve had the Bank of England talking about rates over two weeks ago, these trades were going on and today with extra spike in yields that is just adding fuel to that sort of asset reallocation," said Keith Temperton, sales trader at Forte Securities. Meanwhile, Britain"s post-lockdown economic recovery avoided losing further momentum in September but companies increased prices at the fastest pace on record, adding to signs of rising inflation, a survey showed. read more The domestically focused mid-cap index (.FTMC) advanced 0.3%. Baker and fast-food chain Greggs (GRG.L) provided the biggest support, rising 11.1% after it raised its full-year profit forecast despite supply chain and staffing disruptions. read more A jump in oil prices to three-year highs also supported the benchmark index, although it also fuelled inflation worries. The FTSE 100 index has gained nearly 9% so far this year on support from accommodative central bank policies but has traded range-bound around the 7,000 psychological level since August. The index is around 10% away from its pre-pandemic peaks and its performance below par compared to its European regional and global peers. "There"s still massive economic risks mounting in the final months of the year and I think it"s going to be an interesting test, but the markets are only going to pull back so far before it generates interest once more and I think we"re now approaching that point," said Craig Erlam, senior analyst at Oanda. Britain"s auto sector (.FTNMX401010) dropped 1.2% after preliminary industry data showed new car registrations marked the weakest September for at least 23 years. read more Melrose Industries (MRON.L) declined 1.1% after saying the global chip shortage led to a surge in monthly cancellations from its customers in the auto industry. read more