Conservative Lord Cormack described the bill as “largely unnecessary, narrow, mean-minded" and “in danger of breaching not just international law but also international humanity”.
The High Court ruled that a controversial Home Office policy broke the law and breached the European Convention of Human Rights.
Médecins Sans Frontières branded votes in the House of Commons on Tuesday night “shameful”.
Just three Conservative MPs voted against the offshoring plan, while Edward Leigh urged the government to "hold the line".
“Prit Patel is winning, we’re not going to be getting many people into our country despite the fact that one hundred and fifty thousand people have volunteered to open up their homes."
"This is the most British burn possibly ever,' wrote one person after reading the letter.
The comments were applauded by the crowd gathered inside London's Royal Albert Hall.
"People across the UK have said loud and clear: we want to welcome them, with open arms. Just as we welcomed refugees of other conflicts in the past," the Lib Dems leader said.
“It’s just as confusing on the ground as it appears to be back home", BBC correspondent Phil Mackie said.