"It is likely to be in early 2006," Straw told the BBC on Friday.
He said the vote could not be held prior to that "for the simple reason that in the autumn of 2005 we have the presidency of the EU, and it would be practically impossible to combine both running the presidency with a referendum. That's true for any government".
Britain "won't necessarily be the last of the member states" to hold the referendum, Straw added.
Straw was speaking from Rome, where EU leaders were on Friday to sign the constitution, a first-ever agreement which aims to streamline EU institutions and prevent decision-making gridlock in a bloc which grew from 15 to 25 members this year and is set to expand further.
The text has been accepted by all member states, but must be formally adopted by them - either by a referendum or a parliamentary vote - before it can come into force.
Britain's position is crucial because, as EU officials say, while the process could survive if one or two smaller countries reject the text, rejection by a major power would lead into uncharted territory.
Streamlining EU institutions is
one of the constitution's goals
In a major political U-turn, Prime Minister Tony Blair pledged in April to put the constitution to the British people as part of its ratification process, despite opinion polls indicating they would vote against it.
The Blair government had set no date before the election but had indicated it would follow the next general election, expected in the first half of 2005, and after referendums in at least some other EU states.
A poll published in early September found 41% of Britons opposed the EU constitution, compared with 31% who were in favour of it.