The FTSE 100 index closed down 181 points, or 2.8%, at 6,211.64, the biggest one day fall since June 2013.
Shire led the way down after US firm AbbVie said it was reconsidering its takeover offer for the UK drugs firm.
AbbVie is rethinking its bid in light of new US tax rules to crack down on US firms moving abroad to avoid taxes.
Shares in Shire dived 22%.
Shares in AstraZeneca, which fought off a takeover bid from US firm Pfizer earlier this year, fell 3.2%.
Pfizer had also been intending to move its headquarters to the UK if it had bought AstraZeneca, and there had been speculation that it might come back for a second takeover attempt.
On the upside, Royal Mail was up 1.9% after revealing plans to sell an old mail centre based in London to a hotel and property company for Â£111m.
In the FTSE 250, shares in UK chipmaker CSR surged 30% to 855p after it agreed to be bought for $2.5bn (Â£1.6bn) by Qualcomm.
Qualcomm, which is the world's biggest mobile chipmaker, will pay 900p a share in cash for CSR.
Balfour Beatty shares jumped 5.3% after the company appointed Leo Quinn, head of defence technology firm Qinetiq, as its new chief executive.
Balfour has not had a chief executive since May and has issued a number of profit warnings this year.
Shares in Qinetiq fell 11.8% on the news.
Oil prices continued to fall, with Brent crude dropping below the $84-a-barrel mark. Brent fell to $83.37 a barrel, before recovering slightly to $84.70. US crude fell to $81.56 a barrel.
On the currency markets, the pound rose 0.36% against the dollar to $1.5961, and fell 0.65% against the euro to â‚¬1.2483.
(Close): London's leading shares fell sharply, along with other major global indexes, as fears about global economic growth undermined investor confidence.