Try a product called Grazers. It an odourless chemical which is sprayed onto plants to imparts a foul taste and discourages, well, grazers. It is claimed to work against rabbits, pigeons, deer and geese. I've used it against rabbit damage in my own garden and it did work. They bite off foliage, start chewing then spit it out. I found chewed and discarded shoots on the ground and some plants which had been getting hammered were left untouched after treatment. Whether it is equally effective against deer I don't know, but its worth a try. Google it or try the local garden centre.
Other than that a fence really is the only defence against marauding fallow. In the New Forest, even shooting would be like trying to hold back the tide. As with rabbits, you can never get them all and it only takes one or two to creep in for one night to wreck a garden. Much better to keep them out in the first place.