Group of Seven finance officials also pledged "appropriate", unspecific policy moves as the coronavirus spreads around the world, hitting sports events, trade exhibitions and other large gatherings worldwide.
Britain's blue-chip index ended the day 1% higher, while the domestically focused mid-cap index rose 2%.
Banks ended the day in the red, down 2.13%, while miners <.FTNMX1770> and airlines <.FTNMX5750> up between 2.2% and 2.8%, after they were caught up in last week's rout that erased over $5 trillion from global equity markets. [MKTS/GLOB]
"Global central banks, while not equipped to deal with a pandemic directly, have the tools to short-circuit the brutal sell-off," said Vishnu Varathan, head of economics at Mizuho Bank.
Australia's central bank cut interest rates to a record low on Tuesday, while those in Japan, Britain, France and the United States have signalled willingness to inject more cash into the system.
But analysts have expressed doubt about the efficacy of interest rate cuts amid severe disruptions to the supply chain. Several multinational companies including Rio Tinto and Diageo have flagged a hit to profits this year.
"A Fed rate cut of 50 basis points rate won't get people on planes, it won't get people out spending money at a time when potentially people are going into quarantine and people are avoiding large groups," CMC Markets Chief Market Analyst Michael Hewson, said.
"So this rate cut, while being treated as a positive by the markets in the short term will obviously raise the question: What is the Fed afraid of?" he added.
Britain unveiled its "battle plan" to tackle the spread of coronavirus on Tuesday, warning that as many as a fifth of employees could be off work at the peak of the outbreak.
Marketing firm 4imprint Group jumped 15% after saying it had so far seen minimal impact from the health crisis.
Aggreko, the world's largest temporary power provider, surged 5% and was eyeing its best day in over seven months as it kept its 2020 targets and said preparations for the Tokyo Summer Olympics were "progressing well".
By Devik Jain and Noor Zainab Hussain
