The Lib Dems have been touting themselves as the only party to properly oppose Brexit ever since the referendum. Labour meanwhile have seen their so-called heartlands vote for Brexit in huge numbers and, rather than accelerate the speed at which their vote share is falling in those areas, they have broadly supported the public decision, albeit with some notable caveats.
But let's go back a little bit to examine whether the Lib Dems have a right to be so proud of their position.
Back in 2010, we had a hung parliament: the Tories failed to win a majority at a time when most of the media were backing their claim that Labour's spending had crashed the economy (and most of the media still does, even though Tory austerity has made our economy worse). The heroic Lib Dems stepped in and joined forces with the Tories, bringing us a mostly Tory government with decidedly Tory policies. As the anti-immigration voices from the right (UKIP and a few swivel-eyed loons on the Tory backbenches) got louder, the Coalition government chose to tag along, with plenty of anti-immigration rhetoric, vans telling people to go home etc. They did not oppose the lie that immigration was having a negative effect on the economy; it suited them to allow people to believe it was that rather than their woeful management of the the country's finances. The Tories, desperate to appease the far-right and take the blinkered flag-wavers' votes for themselves, pledged to hold the EU referendum. Right up until the election, Lib Dem junior ministers continued to act as a shield, regularly taking the flak for failing Tory policies and in the general election in 2015, they were completely trounced, losing the vast majority of their seats to the SNP in Scotland and the Conservatives in England. The Tories secured a majority and despite UKIP's expected surge failing to materialise and reneging on a lot of their other promises, the referendum went ahead.
So you see, without the Lib Dems, we wouldn't have had the referendum at all.