The spokesman said the Labour Party would propose the same "basic terms" as Britain's current relationship with the European Union during a transition period following Brexit in 2019 and after that for all options to be open.
Labour's leadership has been criticised by opponents for a lack of clarity on what deal Britain should seek immediately after the EU. He says that should avoid a "cliff edge" situation for the British economy. "It means we would abide by the common rules of both".
Chuka Umunna, a Labour MP and supporter of Open Britain which has advocated a soft Brexit said: "This will rightly pile the pressure on the government to put membership of the single market and the customs union at the heart of their negotiating strategy".
"What Keir Starmer is talking about is protecting our interests during the transitional period after leaving only, not presenting a back door opportunity to stay in the Customs Union or Single Market, and I will be pushing for that transitional period to be as swift and short as possible".
"It leaves unresolved some of the central issues the referendum exposed - in particular the need for more effective management of migration, which Labour recognise must be addressed in the final deal".
Sir Keir also suggested that the United Kingdom may never have to leave the European Union single market if Labour wins the next election, claiming it may be able to persuade the bloc to give Britain the ability to curb immigration from other member states.
'It also means that Labour is flexible as to whether the benefits of the single market are best retained by negotiating a new single market relationship or by working up from a bespoke trade deal'.
The government has advocated a transitional period lasting no longer than the next election - scheduled for 2022.
But chancellor Philip Hammond and trade secretary Liam Fox said the United Kingdom would be "outside the single market and outside the customs union" during this period.
Sir Keir said the Tory approach is an "unnecessary and highly risky path to take", just as his opposite number, Brexit Secretary David Davis, prepares to embark on the latest round of talks in Brussels with the EU's chief negotiator Michel Barnier.
Britain voted to leave the European Union in June 2016 but did not trigger the formal two-year exit process until March.
The government said this week's negotiations were "likely to be technical in nature", ahead of more substantial talks in September.