Not going to happen - for a start there are loads of people who aren't even legitimate voters signing that (amazingly, anyone can sign the thing, it's not IP sensitive - so you could sign it if you want).
Secondly, and my opinion was always that 'article 50' the big red button that starts the withdrawal from the EU, will probably never get executed, because some kind of deal will be made, like is always the case in big politics. The referendum wasn't legally binding - which I am still having diffuculty understanding. Only laws passed by the house of commons and house of lords is.
I spent a couple of months in California in 2007, and it was $2 to £1... looking at it today it's $1.295 to the £1... the pound is suffering badly, and there is simply nothing we can do about it. The stock market however, didn't get too badly thrashed.
I predict interest rates being dropped from 0.5% to 0.25% or 0, and then when the country starts falling apart, they are going to have to raise those again - hopefully not too high, as that will make literally tens of thousands of people default on their mortgages, and lead to a civil war. We just came out of 5 years of QE, printing money wholesale and a very deep recession. Things were just ramping up, and then this all happened.
I really don't know why so much of the world has a soft spot for us; we don't really deserve any special treatment. We are a successful country, we do do things in a certain way that has this honesty and 'old school' properness about it, but let me assure you, we have as much dirt on our hands as all the other major economies, and the old empire went many many years ago.
... don't worry, the US said they would still be our friends.