All airlines worldwide are bound by the Air Navigation Order Carriage of Dangerous Goods Act (amongst others) that was originally formulated at the end of WWII....... Amongst many other things, the Act forbade carriage of any calibre firearm that had ever been adopted as an official military calibre anywhere, ever. This obviously included calibres such as .308 & 30.06 etc.
Some airlines, notably American ones took a sensible attitude to the restriction & ignored it. Others, notably BA enforced it rigorously.
However, the good news is the Act was finally changed about 2 or 3 years ago & BA will now carry these calibres. You should check their website before you travel to ensure nothing has changed & as has been said, BA require 72 hours notice of travel with firearms...... It's advisable to get written proof or acknowledgement from the airline or travel agent of this & be sure to take it with you when you travel.
Note:
Airlines classify firearms as either sporting firearms which they are allowed to transport & weapons of war which they are not. Therefore, always be sure to refer to your firearms as sporting firearms & not as anything else...... especially not as weapons.
BA staff are often not the most educated about firearms so try not to confuse them.
Oh & it's a 5 kg max on ammo per passenger & allowances may not be combined.
Also all detonators, black powder & black powder substitute that are classified as any type of explosive (as opposed to flammable) may not travel under any circumstances, ever.