At the end of the day, it was obvious that the Sterling and FTSE were going to get a hit from BREXIT. The yes vote was unexpected and hence also a double shock. The markets (people rather) react to uncertainty and can easily get spooked. Doom and Gloom reporting only exacerbates the volatility.
Investors prefer the EU, because it makes life easier. Much like non EU countries like the USA and Australia preferring to deal with the EU rather than individual countries. Doesn't mean Britain will be overlooked because that is not true. FTAs will be made with Britain as well and I believe these countries are already working on it in anticipation of BREXIT.
What the markets don't like is uncertainty and instability. Once Britain has a road-map towards BREXIT, then the market will adapt and there will be a soft landing. Theresa May has already divulged that Article 50 will be invoked by March next year. This is a good move. The market has time to adjust.
So of course between now and then, expect some additional volatility on the FTSE and with the Sterling. It will be short lived. Once all the uncertainties are eliminated, then its business as usual.
Worst case scenario is that BREXIT takes another 2 years to complete from the date Article 50 is invoked. which means it will take up to about 2.5 years before we see the Sterling back up to normal levels (and that in itself is speculation). in the meantime, its not all bad especially for exporters who are now better placed to sell products and services overseas. Someone always ends up making money, and that means more exports, more jobs, and more money coming into the UK.
Whenever there is a fluctuation like this, there are always some winners and losers, and the same when the Sterling increases in value, you again get winners and losers.