The FTSE 100 added 0.5%, while the mid-cap index, which rallied on Monday after Brexit Party chief Nigel Farage said he would not fight Conservative-held seats in next month's British election, rose 0.1%.
However, gains for the more domestically-focused mid-cap index were limited as sterling, which had hit a six-month high earlier this week driven by political news, weakened during the day.
Markets rallied last week on signs of a thaw in relations between Washington and Beijing, but those gains were reeled back on Monday after U.S. President Donald Trump cast doubt on the progress of negotiations.
Despite nervousness surrounding the outlook for global growth, sentiment around the U.S.-China trade rhetoric softened with two of Wall Street's benchmark indexes scaling record highs before Trump's speech at the Economic Club of New York on Tuesday. [.N]
Vodafone touched its highest level in a year after it increased annual profit guidance, reflecting improving organic growth trends as difficult markets in Spain and Italy start to ease.
The world's biggest credit check firm Experian climbed 2.5% after it upgraded its organic revenue growth target on the back of strong results in its main North American market, while industrial software company AVEVA added 3.5% after upbeat earnings report.
Support services company DCC, however, slid 6.2% after first-half profit dropped as volumes fell at its business that sells transport fuels and commercial fuels.
Reflecting market's enthusiasm around trade talks, investors moved away from safe haven gold, leading to a 5% drop in shares of precious metals miner Fresnillo.
Industrial distributor Electrocomponents weighed heavily on the mid-cap index, slumping 11% after a 10.4-million-pound writedown in relation to British Steel's liquidation hit first-half earnings.
Discounter B&M European Value Retail fell 6%, after it said it was undertaking a review of its German unit to decide the future of the poorly performing business.
Manufacturing and research company Oxford Instruments meanwhile jumped 10% after reporting a rise in revenue and profits for the half year period.
Among small-caps, Premier Foods leapt 9% after its first-half earnings got a boost from the relaunch of Mr Kipling cakes last year and strong sales of Nissin noodles.
(Reporting by Shashwat Awasthi and Muvija M in Bengaluru; Editing by Uttaresh.V and Angus MacSwan)
By Shashwat Awasthi and Muvija M