Stock markets are partly based on perception of the value of products, and are not necessarily based on the actual value of a product or company. Right now there is growing concern that Brexit will hurt the U.K. including London financially, which is translating into and unstable stock market and could have long term consequences.
To a large extent, unfettered access to European markets and diminished British sovereignty are a package deal. It's never going to be possible for the United Kingdom to retain full control over domestic regulation while enjoying access to EU markets on par with the access available to other EU member states.
The stock market has already shown signs of suffering, and at least temporarily, will continue to do so. It is unclear at this point if this will have a massive, long-term effect or if it will be short-lived, related to panic and uneasiness. Only time will tell if there is a serious impact.
I just don't think the citizens of the UK knew the can of worms they were opening with BREXIT. Yes they had a right to vote for this but no the global market has taken a hit. I am sure the London stock market has been no different and I would be curious to know if that is indeed the case.