Leko met with the Deputy Speaker of the House of Commons, Nigel Evans, on the fringes of a Council of Europe conference of parliament speakers.
Leko told Hina Evans informed him the treaty would be ratified by Christmas and not in the first quarter of 2013, as mentioned at a meeting of EU countries' parliament speakers in Warsaw.
He said Great Britain felt that Croatia was meeting the commitments undertaken in the Accession Treaty.
Leko also met with a Polish delegation, the speaker of the Bosnian lower house, Bozo Ljubic, and European Parliament Vice President Miguel Angel Martinez.
Leko said that Poland, whose lower house ratified the Accession Treaty a few days ago, said the process would be completed next month.
Leko said he and Ljubic agreed that talks should continue on both the Croatian-Bosnian border and the Peljesac bridge.
"I wasn't given a firm assurance that Bosnia and Herzegovina would sign and ratify the (border agreement). As for the Peljesac bridge, we are agreed that it should be built, that's very legitimate and justified."
Leko also spoke at a plenary session of the conference about the crisis of parliamentary democracy. He said the crisis of confidence in politics and politicians was a contemporary global problem and that the transition difficulties in Croatia had further contributed to that crisis.
We are faced with the challenge of how to restore voters' trust in politicians and the representative democracy system, Leko said, adding that it was up to politicians to make sure the system worked for the common good.
It is on parliaments to analyse the problem and propose solutions, he said, adding that the options were modifying or eliminating party slates, introducing the principle of determining the number of deputies based on voter support, and constitutional reform.
The conference continues on Friday, when Leko is expected to meet with Bundestag President Norbert Lammert.