Hi
No, there never was a British Memorial Cross. Only us Cdns and the New Zealanders did them up. Ours are still in existence and only the monarch's inits have changed since WW1.
Closest thing the British had would be the WW1 issue of Memorial Plaque (sometimes called "death plaques" or "dead man's penny" by the callous). Although any Commonwealth fatality would have one issued to his NOK.
Aside from the Memorial Plaque(WW1) and Memorial Cross(WW1 to current), Canada issued a Memorial Bar during WW2.
A fine site about Canadian memorial items, by a true Gentleman, can be found here:
http://members.shaw.ca/jollytar/memorials/memorials.htm
regards
Darrell