Everything imported needs a Vet's certificate, export documentation and customs clearance. Some animals may require import notifications or permits. This is mainly for cats and primates. Providing they are hunting trophies there is no charge for this. If you are bringing home anything else from a taxidermist it will be chargeable.
The size of the shipment depends on how many trophies you have. Dip and Pack skins obviously require less space than mounted trophies.
As a guide I recently brought back a crate with 15 shoulder mounts, 5ft x 3ft x 3ft weighing 250kgs. The cost for flying this to Heathrow (you will need to use an agent here as trying to clear customs yourself is extremely problematic) then onward shipping to my house was £1450, so approximately £100 per head.
When you add this to the cost for the taxidermy in South Africa each head is still approximately 60% of the price you will pay in the UK.
Feel free to contact me for more advice on trophy exporting and shipping.