Hi mate, thanks for your response, it’s a range used by the army, ministry of defence. There very struck of late with certain calibres. 6.5 being 1 of them not allowed.
I only use the Bisley Camp MOD ranges. The safety zones are tested with several parameters for civilian shooters. All ammunition used at Bisley must comply with NRA range regulations, including muzzle energy and velocity limits - not the calibre per se. Although I think .338 LM is not allowed - period - at Bisley for civilian shooter use.
If I remember correctly, the NRA imposes a "high muzzle energy" (HME) limit of 4,500 joules (ca 3,319 ft-lbs) but the use of such a round (as opposed to a calibre) may be permitted if the shooter has undertaken an additional range safety course and follows additional range regulations before use (e.g. proof of zero for the rounds intended for use on the range). There are other HME safety regs. I recall but have not checked that the maximum muzzle energy limit is 7,000 Joules at Bisley for civilian use. There are also velocity limits (mostly applicable to varmint rounds).
So I think the Op needs to do some research into his range(s) regulations. It has been a while since I used my rifles on Bisley ranges so regulations may have changed.
While .308 is the mainstay calibre for F-class, there are other long range target competitions where 6mm and to a lesser extend 6.5 calibre rifles are the bullet/calibre of choice. The graphic below was produced from a survey by precisionrifleblog.com of 200 PRS shooters (300 to 1000 yard targets). Dark row colours represents the ranking of the shooters - darker shades are higher ranking (ie Top 10). This is largely a US universe of shooters although I do think there is now a European competition.
There is a fashion element to these caliber choices with the owners of wildcats calibers often claiming an advantage (bit like Hornady and the Creedmore range). So is a 6mm Dasher better than a 6mm GT or BRA or a 6mm Creedmore - I have no idea - but lots of shooters appear to prefer the 6mm Dasher. I bought a 6.5x47 Lapua (several years ago now) - so clearly that IS and remains the best calibre!

Then working out the optimal twist with tight chamber dimensions for the specific bullet you prefer to shoot while managing recoil..... yada yada yada.....
Given the Ops original 600 yards, target shooting only and the calibers suggested - I would probably choose the .308 for the range and availability of bullets, powders, cases and general knowledge of what it can do. Recognise 30-06 can use same range of bullets. When I last looked at that PRS survey (ca 2016) it was only showing 6mm and 6.5mm calibres
