There are far more Deer around than most people think, add to that that there are gamekeepers and shooters willing to go out at night to keep the numbers of pests (rats/mink/rabbits etc) under control, then there will be times when there are Deer available to take home – most Landowners will keep Red for themselves.
Muntjac are pretty much all over the Country now, and are a real pest for new woodlands. I’d take a guess that the ones in the garden were Muntjac, basically, as one person can pick them up. Red Deer are far too big to pick up alone, and a pain to transport.
BTW, Muntjac is a nice meat, and probably what you’d buy from the local butcher in Southern England, there really arent enough Red and Fallow to supply the meat industry with regularity, but there are loads of Muntjac, and there isnt a season to shoot them.
There are conditions to meet, as noted above, Landowners permission, correct calibre rifle etc, but anyone shooting them will be well aware of this, and is not likely to break the Law doing it, as it is likely they’d lose their Firearms Licence if they breach the conditions.