The Brexit decision cause harm to the world economy, but only in the short term. Long term, the panic will subside and the world will be just fine. Britain was once outside the E.U. and did just fine. It will be fine again once people settle down and let things get back to normal.
The success of the world economy depends on a flow of commerce between nations. The Brexit vote is a dramatic move changing the flow of commerce between the U.K. and Europe meaning that the way commerce has been happening between Europe and the world has changed. Britain has been a significant political and economic member of the EU. Now trade relationships with the EU will likely be re-negotiated because new, separate agreements will have to be made with the U.K.
It is a temporary knee-jerk reaction. The UK has not left yet, nothing has changed and they have up to two years to leave. The election campaign was full of scare tactics which affected voters as well as investors. There was a quick upswing after the tumble and it will continue to recover as people get over the shock election result. The UK is a strong country and economy, they will find a way to overcome any real problems which arise.
I do not believe that the plunge after the Brexit crash will cause harm to the world economy. The stock market goes through fluctuations like this all the time and will again in the future I am sure. It will recover and get back to normal soon. There is no reason to panic.