London's FTSE 100 erased losses to end up 0.2%, while the mid-caps index rose over half a percent. The pan-European STOXX 600 recovered from losses of up to 1.2% to close down 0.1%.
"(Sunak's) announcement highlights the hope that other nations will also remain suitably supportive to avoid economic collapse," said Joshua Mahony, senior market analyst at online trader IG.
Europe's travel and leisure sector, the pandemic's worst casualty, jumped 1.6%, with London's Trainline, bookmaker GVC Holdings and British Airways owner International Consolidated Airlines leading gains.
The German DAX fell 0.1% as a survey showed consumer morale in Europe's largest economy dropped heading into November.
With COVID-19 cases climbing in Europe, all eyes next week will be on the European Central Bank's next move.
Spain became the first Western European nation to exceed 1 million infections on Wednesday, while Italy saw a record rise in daily cases. The number of confirmed cases in Germany jumped by more than 10,000 for the first time in a single day..
Analysts at Rabobank say that while an immediate ECB intervention isn't warranted given the stimulus already being provided, there is now a substantial possibility of an announcement next week.
The broader selloff took a toll on tech stocks <.SX8P>, the worst-performing sector so far this week. Investors have also remained nervous about the slow pace of U.S. stimulus and the Brexit negotiations.
Data showed fund flows into European stocks have surged in recent months as global investors looked away from U.S. equities ahead of the presidential election, and on concerns over high valuations.
Third-quarter earnings continue to be largely better than expected.
French electrical equipment group Schneider Electric SE rose 2.1%, giving the biggest boost to STOXX 600, after it raised its 2020 revenue and margin forecasts.
Unilever rose 0.4% after the Anglo-Dutch consumer group reported a stronger-than-expected return to quarterly sales growth, led by emerging markets.
Swedish hygiene products group Essity and British price comparison website Moneysupermarket.com fell as quarterly revenue suffered from the stay-at-home trend.
(Reporting by Sruthi Shankar in Bengaluru; Editing by Sriraj Kalluvila and Jan Harvey)
By Susan Mathew and Joice Alves