.22 Hornet is remarkably popular, known there as the 5.6x36R.
In fact, rimmed cartridges are remarkably popular, especially in Central Europe where drillings, bergstutz (over under rifle shotgun combos) and single shot break actions are quite popular. The 7.62x51R remains a very popular round as well. We know it as the 30-30. The 7.62x51 is our rather more potent .308. 6.5x55 is still quite popular especially in Scandinavia. The Swiss are fond of some fairly bizarre 10mm stuff shot from incredibly ornate Scheutzen type rifles.
Among the heavy hitters, there are numerous cartridges built off the 7x57 cartridge, everything up through the 9.3x57, although the 9.3x74R (based off the Brenekke family of cartridges) is the more popular of that Caliber in Central Europe. The 303 is not particularly popular in the UK and owning a rifle is quite a hassle. 375 H&H remains popular in the UK and I understand that the 7mm Mag has made great inroads of late with the deer stalkers in Scotland. But again, the .22 Hornet and the 22LR remain very relevant in the UK.