Speed limit signs are duplicated in diamonds yes, where there isnt one present the round sign applies however, it also requires special permission from the transport secretary for a tram to have a higher speed limit than other traffic on a road, it should be the same or less.
Trams are specifically exempted in the 1984 law from one way signs as well as local traffic regulations (e.g. limits on weight for local roads (for example limiting weight of vehicles through a village), bus corridors, non-standard road signs, parking restrictions, roads being closed between certain hours of the day, etc..).
The blue vehicle prescription signs are highway signs which apply to trams as well (though you could argue their path is fixed they are still required to obey the signs)
The tram proceed and points indicator signs are actually road signs.
Markings on the road apply to trams as mentioned, boxes, stopping points, etc....
Animal warning signs do apply, I believe there is (or used to be) deer warning ones on the tramway in London on an offroad section.