Prime Minister Alexis Tsipras said on Friday that the vote would not determine whether Greece stayed in the euro zone, but other European Union politicians said a vote against austerity would leave few options.
Yields on 10-year gilts sank below 2 percent for the first time since June 19, and at 1555 GMT were 8 basis points down on the day as they tracked German Bunds <EU10YT=RR>. Five-year yields were down 6 basis points, while 30-year yields were 5 basis points lower.
Markets still seemed to expect Greeks to reject Tsipras's call to vote 'No' to further austerity, said Vatsala Datta, a fixed income strategist at Royal Bank of Canada.
"All bond markets are reflecting some wariness ... and positioning for a bad-event rally ... but I don't think they are fully pricing in that risk," she said.
Ten-year gilts' yield premium over Bunds dropped by 3 basis points on the day to 120 basis points, its lowest since June 23.
Liquidity was very poor due to the U.S. Independence Day holiday, Datta added.
Next week also brings Conservative finance minister George Osborne's first budget since May's election victory, when he will set out more details of how he will cut the annual welfare bill by 12 billion pounds.
Economists also expect the Office for Budget Responsibility to revise down March's 2015/16 public sector net borrowing estimate by around 10 billion pounds ($16 billion), with a knock-on impact on the government's debt issuance needs.
Out of seven primary dealers in gilts who had estimates available late on Friday, the median forecast reduction in gilt issuance was 7.5 billion pounds, with short-dated Treasury bill issuance forecast to fall by 3.75 billion pounds.
The DMO often uses changes in T-bill issuance to soak up in-year changes in government borrowing needs.
But Datta and others said changes in gilt issuance might take more of the strain this time around, as Osborne's post-election budget came relatively early in the financial year, and changes in T-bill issuance might be needed in December to take account of proceeds from government asset sales.
($1 = 0.6423 pounds)
(Editing by Ruth Pitchford)
By David Milliken