RSA shares closed 20.8% lower, making it easily the biggest loser.
Overall, the FTSE 100 share index closed 0.08% higher, or 4.6 points, at 6,108.71.
Shares in the satellite firm Inmarsat rose more than 1% after it announced a deal with Deutsche Telekom to bring passengers in-flight internet.
Deutsche Telekom will supply the 4G, while Inmarsat will supply the satellite access.
Meanwhile, fashion retailer French Connection saw its shares slump 8.9% after earnings showed it had fallen deeper into the red.
The company reported a loss for the first half of the year of Â£7.9m, compared with a Â£3.9m loss in the same period last year.
The chairman Stephen Marks describing it as "a tough trading period".
On the currency markets, the pound was down 0.14% against the dollar to $1.5507 and was up 0.86% against the euro at â‚¬1.3859.
(Close): Shares in insurance company RSA held back gains on the FTSE 100, after Swiss rival Zurich abandoned its bid plans.