The FTSE 100 jumped 1.1%, its biggest one-day rise since early February, while the FTSE 250 climbed 1.3% on its best day in more than four months.
Offering respite to a market that has been roiled by tit-for-tat tariffs in the last week, Trump said a trade deal with China would be reached soon, despite fears about a protracted trade battle.
"There appears to be a degree of calculation going on here in that investors appear to be banking on any increased tariffs being in place for only a short period of time, with a deal being concluded soon after," CMC Markets analyst Michael Hewson said.
"Time will tell whether that belief is prescient or naïve."
Oil majors Shell and BP provided the biggest boosts on the main index as crude prices surged after Saudi Arabia said explosive-laden drones attacked facilities belonging to state oil company Aramco.
Asia-facing financial heavyweights and miners rebounded after steep losses in the previous sessions.
An earnings-laden day also saw support services group DCC among the top gainers with a 3.6% rise, after it posted annual results and guided to another year of profit growth.
A sour spot on the index was telecoms giant Vodafone , which dropped 3.7% to its lowest in a decade after it slashed its dividend to secure enough firepower to build 5G networks and complete its acquisition of Liberty Global assets.
Property developer Land Securities also lost 1.4% after it reported a wider loss due to a steep decline in the value of its assets on account of a string of collapses on Britain's shopping streets.
Among mid-caps, baker Greggs surged more than 15% to an all-time high after it said the popularity of its vegan sausage rolls had continued to grow, leading it to hike its 2019 profit forecast for the second time this year.
Pub owner EI Group jumped 6.5% after it reported a rise in half-year earnings and said a late Easter had given a good start to its second half.
But Renishaw skidded 6.4% to a near two-year low after the engineering group cut its annual profit target for the second time this year.