Other European indices rose also by well over one percent as Wall Street built on the previous day's gains in early New York business, ahead of US President Donald Trump's State of the Union address.
Sterling sank on news that activity in Britain's dominant service sector almost ground to a halt in January, as companies fretted over the nation's looming departure from the European Union next month.
The weak pound boosted London's FTSE 100 because the benchmark index features large multinationals earning in dollars and euros.
"Results from BP and a weakening pound have propelled the FTSE 100 to a fresh two-month high," said IG analyst Chris Beauchamp.
"Equities around the world remain in robust mood," he added.
The IHS Markit/CIPS UK services purchasing managers' index fell to 50.1 -- its lowest level in two and a half years -- down from 51.2 a month earlier. A reading above 50 indicates growth.
Concerns about Britain's impending departure from the European Union dampened demand and caused firms to delay making decisions on new projects.
Later Tuesday, investors will focus on British Prime Minister Theresa May's key Brexit speech in Northern Ireland.
EU president Jean-Claude Juncker will host May for talks in Brussels on Thursday as the two sides seek to save their Brexit deal.
Sterling had won a partial reprieve on Monday after German Chancellor Angela Merkel struck a conciliatory tone over further Brexit talks.
'Warning signs flashing'
Tuesday's services data followed disappointing manufacturing and construction numbers, with analysts declaring that warning lights are flashing.
"The pound has fallen to its lowest level of the day in recent trade after a third consecutive data point from the UK in as many business days has flashed a further warning sign for the economy," said XTB analyst David Cheetham.
"The latest purchasing managers index for the service sector -- which due to its relative size is considered the most important -- has fallen to its lowest level since July 2016, the month after the EU referendum.
"In the initial reaction the pound has dropped back near the $1.30 level and close to its lowest in a fortnight," Cheetham added.
In company news, British energy giant BP topped the FTSE leaderboard after revealing that annual net profit almost trebled to $9.4 billion (8.2 billion euros) last year as oil prices soared.
Profit after tax rocketed from $3.4 billion in 2017, "primarily affected by higher oil prices and favourable foreign exchange" rates, BP said in a statement.
The news sent BP's share price roaring 4.4 percent by the mid-afternoon, and helped other petroleum majors, too.
"BP earnings lifted the oil sector," noted Oanda analyst Craig Erlam.
"Higher oil prices and output contributed to the stunning profit growth, which bodes well for the rest of the sector, especially with prices showing potential for another burst higher."
Asia Reuters
In Asia, Tokyo stocks edged down Tuesday after three straight days of gains, while Australian banks surged on relief that a national inquiry into abuses in the financial sector was not as damaging as feared.
Trade volumes were thin with most Asian markets closed for Lunar New Year.
Japanese, Australian and New Zealand traders were however given a positive lead from Wall Street, supported by hopes for China-US trade talks and a slower pace of rate hikes by the Federal Reserve.
Financial markets in China, Hong Kong, Indonesia, Malaysia, the Philippines, Singapore, South Korea and Taiwan were closed for a public holiday.