In days of yore, lime mortar was the defacto cement of the day. However it is made primarily with slaked lime (which is dangerous if it gets onto the skin--it burns) and sand. The mortar was also laid using "penny joints" i.e. the depth of the joint was a pre-decimal penny thick! There are very few bricklayers today who could work and lay bricks to such a demanding specification. However if you could obtain the services of an 80+ brickie then you may well succeed.
Lime mortar continues to set as it absorbs carbon dioxide and does not set in water, as does cement mortar. I believe lime/sand/cement is acceptable in conservation areas, but best talk to local builing control.