UK regs (not that they apply) state 50mm, this is purely from a safety point of view and not interference.
The idea is that if the insulation on the Band 1 circuit (ethernet in your case) is not rated for Band 2 (mains voltage) then any damage to the mains cable could also bridge the undamaged Band 1 cables insulation and provide your router/pc with mains voltage.
From an interference point of view, ethernet is fairly tolerant. If possible 250-300mm should be adequate, failing that ftp (foil screened cable) grounded at 1 end or steel conduit again grounded at 1 end only will prevent any issues.
Also remember that to get the best possible throughput, the cat 6 should have no kinks or severe bends as it will be operating at rf frequencies and is more of a wave guide than a conductor.
Steve