Baroness Chakrabarti said unelected peers will water down the Brexit Bill
The bill, which was approved by MPs with a massive landslide, will be scrutinised by the House of Lords for the first time on Monday.
And Labour frontbencher Baroness Chakrabarti said the upper chamber will use the "opportunity" to tweak the legislation.
That is the ambition of many people in the weeks ahead
The peer replied: "I believe that is the ambition of many peers of different parties and of no parties.
"That is the opportunity, that is the ambition of many people in the weeks ahead."
Her comments will anger Brexit campagners who want the bill to become law as soon as possible.
The Labour peer is a close ally of embattled leader Jeremy Corbyn
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David Davis has already expressed fears the House of Lords could throw Theresa May's Brexit timetable off-course.
Speaking earlier this week, the Brexit Secretary said: "We'll have some passing backwards and forward – we call it ping-pong."
But he insisted any issues can be "resolved in good time" before the end of March, when the Prime Minister is planning to trigger Article 50.
David Davis has already warned the House could delay Brexit
Ukip MEP Mike Hookem tore into the upper chamber on Monday, saying it was in "desperate need of reform".
He told Express.co.uk: "Here we have a group of unelected individuals serving their views over the those of the people.
"It's time for an elected upper house who represent the people, not the wants of the political establishment."