but how do i make sure that the ground planes ... having distance of 8 mm is not affecting the BLE radio signals ?
The BLE signals will always be affected by any metal structure nearby. But as long as you keep anything which is electrically conductive at least 8mm away from the antenna then the BLE signal will not be affected enough to be problematic.
The best case is of course no conductive parts nearby at all. But that is not possible so you have to compromise. More distance is always better. If you keep at least 8mm distance and make sure that the signals from the antenna can radiate into the surroundings. I mean, do not put your module in a sealed metal box, like a Faraday cage, then the BLE signals cannot get out. But as long as the signal can "escape" it will work.
Plastic hardly affects signals in the BLE frequency range so any plastic box will be fine but watch out for plastic or paint containing metal particles (like the metallic paints on cars).
Measuring or simulating how your PCB structures affect the antenna is work for EM-field and RF specialists. But don't worry about it too much, follow the manufacturer's guidelines and my suggestions and your BLE will work fine.
BTW, the BLE antenna will not be on-chip but it will be a "chip antenna" on the module. For BLE the frequency (2.5 GHz) is to low to put the antenna on chip. OK, it is possible but not cost effective as the antenna would make the chip too large and expensive.