The comments sent the value of the US dollar higher, which hit the price of oil and other commodities.
This affected shares in mining companies, who were among the biggest fallers in the UK market.
The FTSE 100 fell 112.45 points to 6,053.35. Fresnillo dropped 7% and Anglo American dropped 4.5%.
Shares in oil companies were also lower, with Royal Dutch Shell down about 4%.
In the FTSE 250, shares in travel company Thomas Cook sank nearly 19% after it said summer bookings had fallen.
The company said holidaymakers were avoiding Turkey because of safety fears, while travel to Belgium had also seen a "sharp decline in demand" after the Brussels attacks.
The travel sector was also under pressure following the news that an Egyptair flight carrying 66 passengers from Paris to Cairo had disappeared.
Shares in travel firm Tui dropped 1.7%.
On the currency markets, the pound was boosted by news of stronger-than-expected retail sales growth in April. Sales volumes rose 1.3% from the month before, according to official data.
The pound was down 0.1% against the dollar at $1.4584, and 0.03% higher against the euro at â‚¬1.3017.
(Close): The market dropped sharply as investors reacted to comments from the Federal Reserve which suggested a US rate rise could come as soon as June.