While political developments this week indicated lawmakers are increasingly reluctant to go for a hard Brexit, the lack of clarity on an alternative plan has limited sterling's gains.
"Yesterday's events indicated a further narrowing of the options and longer odds on a hard Brexit but we are still far away from a solution which is capping the pound's gains," said Neil Mellor, a senior FX strategist at BNY Mellon in London.
The pound rose for a fourth day, climbing 0.2 percent to $1.3192. Against the euro, it strengthened slightly to 85.28 pence.
The legislation, put forward by senior Conservative and opposition Labour lawmakers, was rushed through the House of Commons in less than six hours. It was approved at the final stage by 313 votes to 312. It now has to pass the upper chamber, the House of Lords.
Opposition Labour leader Jeremy Corbyn said on Wednesday that Prime Minister Theresa May had not moved far enough in a first round of crisis talks aimed at breaking the domestic deadlock over Britain's exit from the European Union.