Ministers are reported to be pressing for a stronger international stance against Russia.
The UK Government is said to want to use G7, G20, NATO and European Union meetings to urge other countries to take a 'get tough' stance on Russia - despite pressing ahead with plans for a hard Brexit that will weaken British influence on economic and security policy.
Commenting, Stephen Doughty MP, leading supporter of the People's Vote campaign, said:
"If there is one thing Vladimir Putin fears it is Britain acting strongly in the European Union and in NATO.
"So if Ministers wanted to show the Russian president they were serious about defying his attempts to destabilise the western alliance and to interfere in Britain, they would back a People's Vote on the final Brexit deal, and make it clear that while Brexit is a big deal, it is not a done deal.
"Putin treats democracy with contempt and Russian democrats are likely to find themselves harassed, imprisoned or even assassinated. So what better way of signalling our defiance than backing a People's Vote on the biggest political decision facing Britain?"