There are already close parrallel runways at LGW. Other examples are at Seattle, Los Angeles & Atlanta. You could probably get about 63 movements per hour, around 15 more than currently possible in mixed mode operation. I'm no expert but I'm sure that a passing ATCO can help out. This could be achieved without laying any additional concrete and could be a relatively painless way of increasing SE runway capacity.
I remember that I did an M.Sc. thesis on the future role of Gatwick airport fifteen years ago and came to that conclusion then, but no ones taken any notice yet!