The FTSE 100 closed down 1.3% at 6,104.11 points.
The Fed made it clear that worries about the global economy had influenced its decision to keep rates on hold.
"The outlook abroad appears to have become less certain," said Fed chair Janet Yellen, following the decision.
Commodities shares were among the biggest fallers.
Glencore fell almost 5%, as well as fears about demand from a slow global economy, there was added pressure amid questions about its share placing.
There are concerns that markets could now face a prolonged period of uncertainty as to the direction of US interest rates.
Brenda Kelly, head analyst at London Capital Group, said: "Markets have taken cues from the US, but uncertainty prevails and choppiness is the only certain result. Deflation is a concern. China is a concern, and oil prices look set to take another leg lower."
Premier Oil was down 7% but Rangold Resources was up 4% on hopes there would be an upsurge in demand for precious metals it mines as at times of investment uncertainty some seek out gold and silver perceiving  them as safer places to park their money.
On Wall Street, the Dow Jones was down 1% in afternoon trading and there were heavy falls in Europe.
In Germany, the Dax index fell 3% and France's Cac 40 dropped 2.5%.
On the currency markets, the pound was flat against the dollar to $1.55.8, and was up 0.56% against the euro at â‚¬1.37.1.
(Close): Shares in London and elsewhere fell following the Federal Reserve's decision not to raise rates, as concerns about the health of the global economy are renewed.