The London market quickly regained its nerve
The FTSE 100 index fell about 50 points as news of the incidents filtered through, before recovering to end the day 6.4 points higher at 5,221.6.
Stock markets had feared a repeat of the deadly bomb attacks that hit London exactly two weeks ago.
The fact that no major injuries were reported helped markets bounce back.
Analysts said the Footsie had been "amazingly robust".
"There is always going to be uncertainty in the first few minutes but the market has proved resilient," said Simon Buckingham at stockbroker Gerrard.
In New York, however, the Dow Jones index dropped 61.38 points to 10,627.38 by the end of trade.
Mixed reaction
Traders on Wall Street said unease over the possibility of new terrorist attacks in London had overshadowed positive news of China's decision to revalue its yuan currency.
European shares were also briefly hit by the news of the incidents before recovering in line with the London market.
The Dax index in Frankfurt closed 45.37 points higher at 4,829.87, while the Cac-40 index in Paris closed 7.27 points higher at 4,425.66.
"Police are confirming that it's not on the same scale as 7 July. They're not treating it as seriously as that, and things are calming down a little," said trader Lee Curtis at financial bookmaker Finspreads.
Oil stocks were among those stocks most affected by the news, while British Airways, cruise operator Carnival and InterContinental Hotels were also knocked back on fears about a possible impact on tourism.
However, retail shares proved robust despite fears that the latest incidents could keep shoppers away from the High Street.
Retailers were, instead, boosted by new figures showing better-than-expected growth in high street sales last month.
The FTSE 100 index closed higher today despite of the incidents in London. The markets fell over 50 points when the reports first came out, but recovered later and closed 6.4 points higher at 5,221.6.

The stock market had been expecting another attack and today analysts said the FTSE had been "amazingly robust".

'''Dow Jones keeps falling'''

The Dow Jones in New York fell 60 points today to 10,629.