Stock markets in New York and London climbed to new highs on Tuesday as the Dow Jones Industrial Average surged to its highest closing level and the London market surpassed a level last reached five years ago.

Better-than-expected news from the service sector on both sides of the Atlantic and a resurgence in retail sales in the eurozone bolstered a rise in share values that dates back to last summer when central banks rallied in the aftermath of the eurozone's near break-up.

The Dow closed at 14,254, passing its previous high of 14,164 in October 2007 erasing the index's losses during the financial crisis even as Washington's fights over its debts and Main Street seem far from mended.

Cheered by a strengthening of housing market values hit by the sub-prime property crisis and higher consumer confidence, the US remains hugely indebted and blighted by political stalemate in the capital.

The FTSE closed at 6,432, its highest level since January 2008, with analysts according much of the rise to the hopes of an upswing in global growth and higher commodity prices. The FTSE 100 index is skewed to companies that benefit from the sale of oil, copper and chemicals.

The Dow has not touched such high levels since before Barack Obama's first election victory. Global stock markets went into freefall shortly after, as the implosion of housing market and Europe's woes dragged the world into the worst financial crisis in living memory.

Massive issues remain, however. Unemployment, especially among the young, remains high, and in Washington politicians are still at loggerhead over America's $16tn debt. Last Friday, the government started making $85bn of cuts – known as the sequester – in a move Obama and others predicted would cause widespread chaos and financial hardship. In Europe, US firms including GM and Ford are being hit by the region's continuing economic crisis.

But these are old debates now – and Wall Street doesn't seem to be worried.

The latest figures from the Institute of Supply Management (ISM), released on Tuesday morning, showed positive growth in the service sector. The ISM index stood at 56 in February. Anything above 50 indicates growth, and the number was ahead of analysts' forecasts. US markets were also buoyed by rallies in Europe and Asia. In London the FTSE closed up 86.32 points.

The Dow Jones index has now more than doubled since a low point in March 2009, stunning many market watchers and coming against a still lacklustre economic recovery. Corporate profits hit record highs last year, fuelled largely by cost cuts. Economists and market watchers said the Federal Reserve's massive bond-buying programme has fuelled the market but that beneath that there were concrete signs of improvement.

Signs in the eurozone that its slump has halted and 17 member club could start to claw its way back to growth also buoyed investors. Higher retail sales, while mostly in the northern half of the continent, gave some analysts confidence the situation is beginning to improve, notwithstanding uncertainty following the Italian elections and the worsening situation in Greece and Cyprus.

A mixed bag of recent surveys in the UK showing the manufacturing and construction sectors contracting while the services sector continues a five month growth spurt gave little clue as to the voting intentions of interest rate setters at the Bank of England, who meet on Thursday. They are expected to inject a further £25bn in to the economy, taking a signal from a slump in bank lending, that the financial system needs a further boost in funds.

Analysts Capital Economics said the UK economy is still flirting with a triple dip recession despite the positive news from the service sector.

"Granted, unusually bad weather reportedly knocked the manufacturing and construction sectors, so the economy may end the quarter on a stronger note," it said.

"But a material improvement soon remains unlikely, given that the inflation squeeze on consumers is intensifying, overseas demand for exports is fading and another round of austerity begins in April."

Gus Faucher, a senior economist for PNC Financial Services Group, said the political situation in Washington still mattered and warned that if the sequester drags on, the Dow's gains could be at risk. "That said, the fundamentals are better. Profits are at an all-time high, business balance sheets have improved, interest rates are low. The markets are expecting more growth through 2013."

Jack Ablin, chief investment officer at BMO Bank, said investors fed up with low yields from the bond markets were looking for better returns in equities.

He warned that the Federal Reserve's massive bond-buying policy could drive more people into equities. "If you want to see a swift end to monetary easing, another 10-20% hike in the Dow will probably do that," he said.

Minutes of the Fed's last meeting revealed a split in the central bank's rate setting committee. While the Federal Open Markets Committee's members were still worried about unemployment, "many participants also expressed some concerns about potential costs and risks arising from further asset purchases", according to the minutes.

Friday may prove the next test for the markets, and the Fed, when the latest nonfarm payroll figures are released. The US added 157,000 new jobs in January. Average job creation for 2012 was around 181,000, a number just above the benchmark economists calculate is enough for the unemployment rate to stabilise, but not fall. © Guardian News and Media 2013