The Government told the European Commission two weeks ago that it believed the BT Webwise platform, run by Phorm, is legal.
Privacy campaigners have expressed outrage against the technology, which allows ads to be targeted by tracking the websites that users visit.
A statement to London's Stock Exchange by Phorm said: "Following successful completion of this trial and an appropriate period of analysis and planning, it is currently expected that Phorm's platform will be rolled out across BT's network."
A spokesman for BT said: "The trial will work on an 'opt-in' basis only - customers can only take part if they accept the invitation."
The new trial follows a statement from the Department for Business, Enterprise and Regulatory Reform that the service does not breach European data laws.
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