It is a sure sign that a royal romance is serious when the girlfriend is taken stalking. Not celebrity-stalking, of course, but deerstalking.

Photographs showing Kate Middleton in hunting gear, lining up a rifle for a spot of target practice before setting off for the hill at Balmoral, are seen by seasoned Palace-watchers as clear evidence that an engagement to Prince William must be in the offing.

Whereas for most couples the telltale clues include a holiday for two in Marbella, among royalty they feature the crack of a rifle and the gralloching (removal of the stomach) of a stag in the heather. If Miss Middleton has been inducted into what is regarded as the king of sports, then she really has been welcomed into the heart of the Establishment.

Sunday newspapers ran pictures yesterday showing Miss Middleton, 25, in jeans and a camouflage jacket, lying on her stomach in the approved style alongside the Prince of Wales, as she aimed at a target. No proper stalker sets off for a day’s sport without a few practice shots.

Just as inevitable as the speculation was the ritual protest from the League Against Cruel Sports, which accused Prince William of introducing his girlfriend to “a barbaric and unacceptable pastime”. Barry Hugill, of the league, said: “I don’t think the Royal Family does itself any good whatsoever by doing this. Charles and his son have an appalling record of slaughtering animals for fun.”

Yet the league appears to have come out on the wrong side of the conservationist argument. Most environmental groups, including English Nature and Scottish Natural Heritage, believe that there are far too many deer on our hills and have instituted culls. Deerstalking is supported by Scottish Natural Heritage, the National Trust for Scotland, the Forestry Commission and the Deer Commission, so training someone to kill a stag quickly and cleanly should by rights be applauded. Although it prefers the term “deer management”, Scottish Natural Heritage conceded this year that stalking was “an important part of the rural economy”.

If the gossip is true, William may be preparing for a rather different kind of stag night.

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