Rank, which operates 35 casinos and 103 bingo halls in Britain, had said in January that it was in talks with Gala. A potential deal would have made Rank Britain's biggest casino operator.
"Rank remains committed to delivering sustainable growth in shareholder value; the proposed terms of the potential acquisition did not achieve this objective," Rank's Chief Executive Ian Burke said in a statement.
Rank, which is 74.5 percent-owned by Malaysia's Guoco, said it would now concentrate on delivering its organic growth plans, including the delivery of 12 more G casinos by 2015.
Maidenhead-based Rank, which owns the Grosvenor Casino and Mecca Bingo chains, had rejected a takeover offer from Guoco last year.
The company's shares, which have risen 2 percent since late January when the company said it was in talks to buy Gala's casino business, closed at 129.5 cents on Wednesday on the London Stock Exchange.