I will find out for sure, but I seem to remember that 270 & 308 were the most commonly used. North Highland College put the Professional Development Award for Seal Culling.
The shooting assessment is for the shooter to put 3 rounds in a 4" circle at 50 & 100m.
In Norway the minimum calibre for seal is 6,5*55 with a 140 grain bullet. Same as for moose actually. We usually go for head shots, most seals that don`t expire immediately tend to sink, and then recovery is a bitch. Most people that hunt seals would prefer using a 223 or a 22-250 with a vmax bullet, it would minimize the risks of richottes when shooting at sea, and the skull of a seal are paper thin, so a 22 lr would be more than enough to penetrate through the skull.
Seals 13.29 Under the Conservation of Seals Act 1970, seals may be shot by fishermen and others to prevent damage to fishing nets or fishing tackle, provided that at the time the seal was in the vicinity of the net or tackle. Seals may also be shot to prevent damage to fisheries under licences issued by Natural England (for rivers only), the Marine Management Organisation, the Welsh Government, or the Scottish Government (see section 10 of the 1970 Act). No firearm may be used except a rifle using ammunition with a muzzle energy of greater than 600 foot pounds and a bullet weight of not less than 45 grains (see section 1 of the Act). This equates to at least a .22 Hornet centrefire rifle using 45 grain, although this cartridge is, at best, only marginally humane. More information on this subject can be
found within chapter 14
Control of Seals 14.63 Legislation relating to seals is to be found in The Conservation of Seals Act 1970 together with Orders made by Defra. In Scotland, the 1970 Act has been repealed and the protection of seals is now secured under Part 6 of the Marine (Scotland) Act 2010. 14.64 The 1970 Act prohibits the killing or taking of seals during the close season, which is: Grey seals: 1 September – 31 December Common/harbour seals: 1 June – 31 August 14.65 The Conservation of Seals (England) Order 1999 further prohibits the killing, injuring or taking of seals in the counties of England bordering the North Sea: from Northumberland to East Sussex, and adjacent waters throughout the rest of the year. 14.66 The 1970 Act provides a defence for the killing of seals to prevent damage to fishing nets etc. by the owner or a person acting on their behalf, provided the seal was in the vicinity of the net or tackle at the time. The Act does not stipulate whether the fisherman is involved in, or using, equipment for sea fishing only, or whether it also includes freshwater fishing. Section 10 (1) states that licences to kill or take seals in specific areas may be granted by the Secretary of State, with the consent of the appropriate nature conservation body. No firearm may be used except a rifle using ammunition with a muzzle energy exceeding 600 foot pounds and a bullet weighing not less than 45 grains so that any .22 rimfire rifles are excluded and .22 centrefire rifles are required, with the .22 Hornet using 45 grain bullets representing the lowest acceptable combination of bullet weight and energy.