Ministers remain determined to press ahead with plans to scrap the job of lord chancellor and create a supreme court, despite a House of Lords defeat.
Lord Falconer's historic post would be abolished under the changes
Tory and crossbench peers voted 216 to 183 to send the law plans to a special select committee for extra scrutiny.
No 10 described Monday's defeat as a "serious matter" but said that, although it was determined to get the plans into law, it would not rush its next move.
Tories have urged ministers not to try to force the Bill through.
Ministers have said the Lords vote means MPs may never get a say on the plans. They are now pondering what to do next.
The prime minister's official spokesman said: "We still want to progress this matter, we still believe that the
will of the Commons should be heard...
"We are going to take a period for reflection, that is what we will do.
have a very clear idea of how we might progress but I'm not going to rush into
an announcement now."
Lord Falconer, the lord chancellor, told Radio 2's Jeremy Vine show that the reforms were "worthwhile" and blamed an orchestrated Conservative campaign for the vote defeat.
Lords Leader Baroness Amos had earlier said the defeat had "nothing to do with constitutional principle - and everything to do with political opportunism."
The government could decide whether to withdraw the Bill and reintroduce it in the Commons so it can use the Parliament Act to force through the changes.
Tory Lords leader Lord Strathclyde said: "Any suggestion that the views of Commons and Lords on scrutiny should now be bypassed by withdrawing this Bill and laying a new one would be an act of
He argued that it would be "the mark of a government unwilling to listen to the voice of
Alan Duncan MP, the Conservatives' spokesman on constitutional affairs, told BBC News 24: "The House of Lords has done everyone a favour who is interested in seeing a good system of justice in this country."
The Tories deny claims they simply tried to kill the Bill, arguing they just want more time to get the details right.
But Labour backbencher Clive Soley criticised what he described as "a very deliberate attempt" by a large proportion of Tories in the Lords to wreck the government's moves for change.
Mr Soley, a member of the Commons constitutional affairs committee, said the government had to deal with the issue and should use the Parliament Act if necessary.
"We cannot go on with this system where the law lords sit in the same body that makes the laws and, at the same time, that body is still largely unrepresentative of the UK as a whole."
Liberal Democrat spokesman Lord Goodhart said he was angry an important bill had been delayed.
The Bill seeks to establish a new independent commission to appoint judges.
Lord Goodhart said judges believed that was urgently needed as the current system was in "limbo".
The committee of law lords in the House of Lords currently acts as the court for final appeals in the UK.
The proposed reforms would leave that job to a new supreme court working completely separately from Parliament.
The government says that change will protect the independence of the judiciary and set clear boundaries between politicians and judges.
Opening the second reading debate, Lord Chancellor Lord Falconer said the current system had worked well in recent years but one failure would undermine it, he said.
"We should change when we are strong, we should recognise that we can improve the system," he argued, rejecting any suggestion the new court would be "second rate".