In England and Wales, the deer act (1991) specifies that rifles must have a calibre of not less than .240 inches or a muzzle energy of less than 2,305 joules (1,700 foot pounds). While this is sufficiently vague, it is generally accepted that this law requires both conditions to be met, but it has not been tested in court to my knowledge (English law relies on precedent). It applies to all deer species, although it was recently amended to allow .22 centrefire rifles for muntjac and chinese water deer, but not roe (go figure!). I would need to look up the details on energy, etc. specified for .22 centrefire calibres.

On this basis, I think the 6.5x54MS would be legal (or could be loaded as such) for deer shooting in England and Wales.

In Scotland, there is no claibre restriction, but there is a distinction between red and roe deer, and also velocity, bullet weight and energy requirements. Under the Deer (Scotland) Act (1996), a bullet of not less than 100 grains (6.48 grams) with a muzzle velocity of not less than 2,450 feet per second (746.76 metres per second) and a muzzle energy of not less than 1,750 foot pounds (2,373 joules) must be used. For roe deer only, a bullet of not less than 50 grains (3.24 grams) with a muzzle velocity of not less than 2,450 feet per second (746.76 metres per second) and a muzzle energy of not less than 1,000 foot pounds (1,356 joules) may be used.

Because of the velocity requirements, the 6.5x54MS may not be legal for deer shooting in Scotland, but could probably be loaded to meet the requirements.

The primary reason for the introduction of these laws was deer welfare, because until the 1960s they were regarded as vermin with no closed season and most were shot by gamekeepers with shotguns (not rifled slug guns as in the US). However, as with the introduction or amendment of any law, there are always competing interests and a compromise always results in anomolies, such as not allowing 22 centrefires for roe in England, but allowing them in Scotland.

Disclaimer: This information is taken from the Home Office guidance to the police. Please double check with the relevant legislation. Above all don't sue me!