In more serious surveys there is still a real effect, and one I find slightly surprising, eg at the most recent polls reported the methods and results are as follows:
Survation -- Telephone -- Remain +8 ;
ICM -- online -- Leave +2 ;
ComRes -- Telephone -- Remain + 11;
ORB -- Telephone -- Remain + 8;
Ipsos MORI -- Telephone -- Remain + 10;
YouGov -- online -- Leave/ remain tied;
Opinium -- online -- Leave +4;
These patterns generally hold through all polls, although there are some cases where Leave wins over Remain in phone polls; but they are, or appear to be, rarer.
How odd. In both cases the sample is, in principle, random. Perhaps the catch is that YouGov, for example, only conducts surveys among people who have signed up for YouGov, so you had to be interested enough in wanting to take polls to join in... will that skew things so much? No idea.
See also
https://ig.ft.com/sites/brexit-polling/ , which helpfully distinguishes online v. telephone polls graphically.