The move means any agreed solutions to the Irish Border will be given an opportunity to be worked out in full.
They said the position paper's wording was created to allow some flexibility between European Commission's proposed end date of December 2020 and Britain's suggestion of around March 2021.
The EU has said the transition phase should end on 31 December, 2020, the end of its budget period.
"The best way to protect and enhance the high standards that exist in this country is to stay in the Single Market and the Customs Union", which British Prime Minister Theresa May has said Britain will leave, Umunna said.
Sam Lowe, a trade expert at the Centre for European Reform, told the Guardian: "A standstill transition is in everyone's interest and absolutely essential if the government is serious about negotiating a mutually beneficial ongoing relationship between the EU and UK".
There are reports that the worst impacts of Brexit could be delayed for up to two years.
The length of the transition period has become a source of debate since the emergence of a United Kingdom negotiating paper which suggested it could be prolonged indefinitely, although ministers made clear a fixed end date would be stated in any deal, and it would be around two years after formal exit.
A group of pro-Brexit Conservative MPs known as the European Research Group (ERG) also on Wednesday sent a letter to May with a number of suggestions for securing a successful Brexit.
At least the Prime Minister is attempting to be collegiate in her approach as she seeks a broad consensus - perhaps Tony Blair should have done the same before the Iraq invasion of 2003.
"I think there's an important point that EU citizens who come here after we've left the EU will have done so knowing that we're leaving the European Union and will have different expectations to those who have been here for some time and are entitled to settled status", she said.
It said: "The UK believes the period's duration should be determined simply by how long it will take to prepare and implement the new processes and new systems that will underpin the future partnership".
May will retreat to her official country residence with senior ministers on Thursday to thrash out their differences.
The Renew party, founded previous year after Macron's En Marche! movement propelled him to power, said it would target pro-Brexit lawmakers in constituencies with high levels of support for European Union membership.
Britain could be stung with an extra £4-£5 billion Brexit "divorce bill" if a post-withdrawal transition period runs into 2021, MPs have warned.
"To avoid the perversion of democracy that Brexit in name only would be, it is essential that we are able to sign trade deals in the fixed transition period".
The bloc also doubts that is enough to agree a comprehensive future trade deal and expects that time to drag out.