(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window) * UK factory PMI shows fastest growth since 2017 * No-trade deal Brexit is still possible - UK minister * Homebuilders rise as house price inflation jumps * FTSE 100 up 1.9%; FTSE 250 adds 2.6% (Updates prices to close, adds comments) ADVERTISEMENT Dec 1 (Reuters) - Britain’s FTSE 100 and mid-cap FTSE 250 had their best session in three weeks on Tuesday as upbeat Chinese factory data fuelled hopes for a global economic recovery from the COVID-19 crisis. Data showed China’s factory activity accelerated at the fastest pace in a decade in November, while British factories showed their fastest growth in almost three years. The Chinese data drove a surge in Asia-focussed banks , which gained 5.6%, while the blue-chip FTSE 100 rose 1.9%, after its biggest monthly gain in more than three decades, and the FTSE 250 added 2.6%. “The FTSE 100 is a global bellwether so any data that supports cyclical recovery is going to benefit the UK markets,” Oliver Brennan, senior macro strategist at TS Lombard, said. Attention was also focused on Brexit trade talks, with a senior British minister saying there was still a chance of a turbulent divorce without a deal. “A no deal outcome might actually give the FTSE 100 a short-term boost as the likely resulting drop in sterling boosts the relative value of the overseas earnings which dominate the index,” Russ Mould, investment director at AJ Bell, said. The FTSE 100 has rallied nearly 30% from an eight-year-low in March on the back of unprecedented fiscal and monetary stimulus and, more recently, signs that an effective COVID-19 vaccine would be available before the end of the year. But the index is still down about 16% this year, underperforming the European benchmark STOXX 600 index. British house prices rose by the most in nearly six years in November, data showed, lifting the FTSE homebuilders index by 1.9%. (Reporting by Shivani Kumaresan in Bengaluru; Editing by Shounak Dasgupta, Saumyadeb Chakrabarty and Alexander Smith)