How do you know this is a lie? Has it been disproved by anyone?
Obviously since the referendum there will be a higher percentage of brexiteers - although I imagine probably still a minority as we know happens with Question Time.
I suspect that when these people have been on the Today programme it will not always have been in the context of the UK leaving - it could for example have been about the euro crisis or other EU affairs. But for me it illustrates the mindset of the BBC and the type of people they want on. They don't want people on who are opposed to the EU.
They have details on their surveys on here.
http://news-watch.co.uk/monitoring-p...s-and-reports/