Movement has been scarce but support for remaining within the EU has generally been higher than support for leaving for most of this year. That's fairly significant considering we're currently in the process of leaving, with that same process being highly criticised. It's also fairly notable considering neither of the main two parties are advocating remaining within the EU currently: the government continue to advocate a well-managed exit (even if they're incapable of it) and the opposition are at best tacitly wary of leaving, and generally supportive of doing so.
I do think there's something strange in those on the left defending Labour's stance on this based on polling when it was perfectly convenient for that to be ignored when Corbyn first came to power. Or when the country was keen on austerity. Obviously Labour need to be smart in their actions and there are risks in going against the vote itself, but the consistent argument from them under Corbyn has been to try and change the outlook of the British public on key issues instead of moving to the centre to accommodate such views. Yet on Brexit, an issue which will inherently impact everything a Corbyn government wants to do, they're fine to use the polling argument.