Any calibre of rifle that is legal to do the job. With a surfiet of energy and weight that is specified by law for the species of deer you are going to shoot ,whether your quarry is in Scotland or England as the criteria on either side of the border is different,
What is acceptable in Scotland is not acceptable in regard to roe deer for instance using smaller calibres and in England smaller centre fire rifles may only be used on Chineese water Deer and Muntjac whereas in scotland the smaller centre fires such as 222 or 22-250 are legal on Roe deer and more than proficient to cull Roe deer