The blue-chip FTSE 100 index slipped 0.4%, with financial and material stocks weighing the most, while the domestically focussed mid-cap FTSE 250 lost 0.9%, ending at a nine-day low.
Hancock's announcement followed Finance Minister Rishi Sunak's grim forecast on Wednesday that Britain was set for its worst annual economic contraction in more than 300 years due to the pandemic.
Britain has Europe's highest official death toll from the pandemic and has been hit hard by a second wave of cases, which prompted a month-long lockdown that has severely crimped economic activity.
"There is a tug of war between the short-term uncertainty, what is going to be a tough winter from an economic standpoint and the potential for a much stronger and sustained recovery, if we get mass vaccination and the pandemic is brought under control at some point next year," said Emmanuel Cau, head of European equity strategy at Barclays.
While positive vaccine-related headlines have helped British stocks gain this month, they have still underperformed global peers due to uncertainty over Brexit negotiations, as the end-of-year deadline for a trade deal looms.
Britain and the European Union can clinch a Brexit trade deal and the shape of one is clear, but London will not sign up to an accord at any cost, Finance Minister Sunak said.
Among individual movers, homebuilder Persimmon and fund manager Intermediate Capital Group bottomed out the blue-chip index.
Retail banker Virgin Money UK was among the biggest weights on the mid-cap index, dropping for a second straight day after reporting a 77% drop in its annual profit.
(Reporting by Devik Jain in Bengaluru; Editing by Subhranshu Sahu and Bernadette Baum)
By Devik Jain and Ambar Warrick