The FTSE 100 closed up 1.2% to lead gains among European peers. The index extended gains after the UK announced new restrictions on Tuesday but held back from imposing a full lockdown.
Johnson's comments came ahead of an update due on Thursday from British finance minister Rishi Sunak on the economy and the government's plans to protect jobs.
"The promise of a package reassured markets that jobs will be secured in some way, serving as a precursor to more severe measures that will likely be announced in the coming weeks," said Connor Campbell, financial analyst at spread better Spreadex.
Healthcare stocks led the rally in UK, while JD Sports topped the blue-chips index as sports companies across the globe got a lift from Nike's stellar quarterly results.
Glencore weighed on miners as a slide in iron ore and copper prices weighed, while oil stock were hit by BP's 1.2% decline.
Meanwhile, Britain's recovery from the coronavirus lockdown lost some momentum in September, a business survey showed, as consumer-facing sectors suffered from the end of a government subsidy to support restaurants and more general COVID-related worries.
A weaker pound and a raft of stimulus measures have helped the FTSE 100 bounce back from its coronavirus-driven slump in March. However, an increase in COVID-19 cases and the UK's economic weakness has kept investor optimism in check.
The mid-cap index broke a five-day losing run to end up 1.0%.
Topping the index were restaurant chain owner SSP which rose on indications of a recovery in sales, and technical products maker Diploma which surged on a deal to buy a U.S.-based wire and cable distributor..
By Susan Mathew and Shashank Nayar