Will the Brexit actually take place???

It is not a certainty...

The referendum voted for the exit, but the government is not bound to the referendum result. The result was close and the fallout has been considerable since the result was handed down. Many Brits who voted for the exit may be having second thoughts when they realize all imported goods will cost more and that Great Britain may not be so great when all the dust settles. Is it all worth it, they may ask themselves? Furthermore, the EU may offer the Brits some sweeteners to remain; sure as eggs are eggs, they would like them to stay.

Another vote may see a vastly different outcome. I suspect it's no guarantee we have seen the last of this discussion...