I think the bounce back has been caused by people getting over the initial panic and realising that any actual change won't happen for more than two years. In the mean time, the UK stock market wasn't over-valued prior to the referendum at all and the weakened Pound helps exporters, so in the short term there is literally no bad news.
Prominent UK politicians have stated that they want to stay in the single market, but they want to control immigration. The EU have emphatically stated that there is no access to the single market without free movement of people, so basically UK politicians have to back down on one of their two demands.
If the UK turns its back on the single market, no one really knows what will happen. New deals could be better for the UK or could be worse, but several businesses have stated they would reduce UK operations if this happened so the bare minimum would be short term pain for investors into the UK.
If the UK settles on a Norway type deal, with access to the single market and unrestricted immigration, then this is literally business as usual for the UK and this whole painful, volatile process will not have changed a damn thing. If this happens, there will be a huge backlash from the public who voted for leave. I'm not thinking riots here, but civil unrest is possible.
My personal opinion is that the UK will end up in the EEA, which is the best outcome for businesses/investors. This will happen because UK politicians will be able to "save face" by blaming the EU for being "unwilling to negotiate" on immigration where as leaving the single market will mean that dismantling the UK (with Scotland and Northern Ireland going their own way) will always be the current crop of politicians legacy, with no one to blame but themselves.
The worst possible outcome, in my opinion, would be a second referendum where the public are asked to choose between the two options I listed above. This would be spineless of the politicians (who are getting paid large salaries to make the difficult decisions on our behalf) and I think the British public has already proven over the last week that they can't be trusted to make a decision in their own best interests.