The House of Lords will start debating the Article 50 bill on Monday with amendments tabled to guarantee the rights of European Union citizens in the United Kingdom, for greater scrutiny on the process and for a "meaningful vote" at the end of Brexit negotiations.
Theresa May quickly attracted the attention of peers and journalists as she sat on the steps of the throne, with a small group of other MPs.
MPs in the House of Commons have already given their go-ahead to the so-called Brexit Bill, which gives May the authority to invoke Article 50 of the Lisbon Treaty to initiate Brexit negotiations.
Speaking to BBC Radio 4's Today programme, she said: "The focus will be in the next couple of weeks in the House of Lords on the process of the Prime Minister and her negotiating team to come back to parliament".
"We want to get Britain to a staus of being an independent country... and getting those trade deals".
The Prime Minister's spokesperson told journalists that Ms May was sitting in place "in recognition of the importance of this Bill as it proceeds through the Lords".
Britain's upper house, the House of Lords, on Monday begins debating legislation to empower May to trigger Brexit.
The Conservative government presented the short bill after losing a high-profile court battle in which judges ruled that May must have parliament's consent before beginning the UK's departure from the EU.
The House of Lords, the unelected upper chamber in the British Parliament, are seeking to delay and amend the Brexit bill passed in the elected House of Commons.
Five days have been set aside for the so-called Article 50 bill to be debated and scrutinized by the House of Lords.
"If we ask the House of Commons to look again at an issue, it is not a constitutional outrage, but a constitutional responsibility", Smith said.
In the debate, she added: "We will not block, wreck or sabotage the legislation before us".
"Whatever our personal views, disappointments and genuine concerns for the future that is not the role of this House".
"But, I've also said, neither should we provide the Government with a blank cheque". If the Lords change the bill, it will return to the Commons; That can lead to a process known as ping pong in which the bill can go back and forth between the chambers several times before consensus is reached.
He said: "When a deal is reached the country is entitled, either directly or through Parliament, to pass judgement on what's on offer". He highlighted the historic support of David Davis, the Brexit secretary, for what he used to call a "decision referendum".