All this speculation is pointless- all we know is that it will come into effect in the summer. To people who say it can't happen on June 1st: on what basis? They could always say the rules will come into effect the following week. I'm not saying that's what will happen but it's likely it will take effect between June 1st or July 1st.
Just a guess: I think it will come into effect by July based on google searching so much on this topic. There's a near consensus among lawyers, consultants etc that it will be in effect by July, which gives the Tories 3 months prior to elections to show that they're taking action on citizenship/immigration and any speeding-up in processing would be used as election propaganda. Just my 2 cents.