A Lib Dem peer has been tempted by Theresa May to switch to the Tories.
Zahida Manzoor said she was impressed by the Prime Minister's talk of promoting social mobility.
"Leaving the Lib Dems, where I've been a member for three years in the House of Lords, was tough, but it was the right thing to do. I could not support the leadership of a party that calls itself democratic and then refuses to acknowledge the will of the people in a referendum," she said.
"Theresa May's vision of a Britain that works for everyone, and her clear leadership over Brexit, now make the Conservatives a natural home for me and millions of people like me, from all communities across the UK.
"As Britain embarks on a new journey, outside the EU but reaching out to trade with the world, and as we really begin addressing the problems of social mobility at home, I look forward to helping play my part as a Conservative," Baroness Manzoor added.
Lib Dem leader Tim Farron told BBC One's Sunday Politics that his party had gained 20,000 new members since June.
This included thousands joining from the Conservatives, including hundreds since its party conference, Mr Farron said.
"I'm always sad to lose people, but I'm overjoyed to gain 20,000 times more people than I've lost," said Mr Farron.