As a comparison, see how easy a ride the Tories have had with dodgy Russian money and connections, even after the actual security services have explicitly warned about the individuals various Tory ministers (right up to and including the PM) and supporters have been consorting with. With one Russian being ennobled after the head of MI5 declined a meeting with him, set up by Tory supporters, because of suspicions about his intentions and wanting to keep the UK security institutions clean of foreign (and specifically Russian) influence. Nothing about that from the Tory media though. Nor the 600k that Barclays flagged and that the NY Times traced to a Russian account. Even when foreign media have done the legwork, even when the services officially protecting our country express concerns, our right wing media will still look the other way, thus allowing them to shape voter opinion to continue supporting their dodgy politicians.

About the immigration to Leave switch: I can't remember if I've posted it here, but there's a record of UK national issues polls, either by yougov or someone equally credible, which asked people what their main concerns were at that particular time. Immigration was in the top 1 or 2, averaging 20-30% (the other top 3 concerns being economy and NHS also averaging similar numbers), with the EU being nowhere (averaging around 1-3%), right up until around Feb 2016, when the EU jumped up to 1st with around 30-40%, and immigration disappearing as an issue.