Shares in London's FTSE are down 13.7%, the worst quarterly performance since 2002.
Friday's falls follow an unexpectedly sharp rise in the eurozone inflation rate for September to 3%.
Investors had hoped the European Central Bank would move to lower interest rates in the eurozone, after raising them in July to 1.5% to limit inflation.
However, the latest inflation figures may make such a move less likely.
Wall Street's main Dow Jones index ended Friday trading down 2.2% to record its worst quarterly performance since 2008.
Eurozone worries
But Friday's falls were just the latest bout of volatility in European markets, which have failed to regain ground since crashing towards the end of July.
Economists say worries over the ability of eurozone countries to pay their debts are sparking concerns of a new banking and credit crisis.
"The euro area debt crisis has potential ramifications to euro area banking sectors in particular," said Grant Lewis, head of research at Daiwa capital markets.
"You've got concerns that a Greek default going wider into something more serious in terms of an Italian default, for example, that would leave banking sectors under-capitalised as well as having a calamitous effect on the economic outlook."
Shares in Germany's Deutsche Bank and Commerzbank both lost more than 30% in value since the end of June.
Stocks in French banks fared even worse. Societe Generale saw its stock fall more than 50%, while BNP Paribas saw its share price fall more than 40%.
The share falls have therefore been most pronounced in eurozone countries, with the FTSE falling less than benchmark German and French exchanges.
Brent crude was also set for the biggest quarterly fall since the financial crisis of 2008.
Oil for delivery in one month's time fell just over 8% to $103 a barrel in London as investors worried about a slowdown in the global economy.
Worries ahead
Global markets have been hit by a 'toxic cocktail' of factors, says one economist
Despite the record quarterly falls, markets remain up on the levels they reached after the 2008 financial crisis.
"There are certainly widespread indications of pretty serious financial stress, but they are not by and large as dramatic as they were in 2007 and 2008," George Magnus, European economist at UBS, told the BBC.
"Then, the whole edifice of the Western banking system was about to implode. At that point, I think it was far more dramatic than it is now."
But investors and economists fear the situation may deteriorate further.
Markets are likely to look to forthcoming company results and quarterly economic data for their next move.
In the longer term, economists say they are seeking reassurance from politicians.
"I think markets are expecting something of substance to be revealed by the G20 [group of leading nations] in November and if it isn't, we could be in a lot of trouble," Mr Magnus added.
http://www.bbc.co.uk/news/business-15128250