I think you should go for uniquely English rather than British, so not Grenadiers. If you want military, go for an English regiment, perhaps Route Of The Blues , or Warwickshire RHA.
Surely not A Place Called England since it is so unflattering and unkind to the dear old place.
The DT gives a hundred or so songs containing the word England, most of them very suitable.
At our singaround session we are just going to insist on songs that are of and from England. This will make it quite an unusual evening. That situation could only be found in England. I am sometimes saddened that English songs are so neglected in England.
Keith.