These are London councillors representing boroughs that were among the large majority of Londoners voting to remain in the EU. Basically, they want Labour to change its mind and oppose Brexit, which anyone in their right minds would do.
They’re not calling for a second referendum specifically, but they do want a rethink.
Whether it’s a final parliamentary vote on whether we do exit Brexit, which seems to me to be the better option, or another referendum (and there are good arguments against, including the one that says the first referendum was a bad idea so a second one just makes it worse), we need a rethink, which is not something the Tories in charge are capable of.
There’s no mechanism built into the UK constitution for government by referendum, and good arguments why there shouldn’t. But there is also, therefore, no reason parliament should regard them as binding. They are just an expensive opinion poll sampling opinion on the day.