They want Her Majesty's Government to become a global leader on the prohibition of wildlife trade and help combat African poaching groups. Since we know how beneficial prohibition is for criminal gangs, the only group rejoicing over this leap forward would be the poachers themselves. The alternative lies in the private sector.
Were I presented with the opportunity to become the Al Capone of the ivory trade, never would the temptation be as strong as now. Governments are immensely successful at making products under prohibition enormously valuable. As Milton Friedman said regarding drug prohibition:
"If you look at the drug war from a purely economic point of view, the role of the government is to protect the drug cartel. That's literally true."
Every time there is a major call for an outright ban on ivory products, prices skyrocket, which ends up incentivising poachers to shoot more elephants. This has created a sort of cat-and-mouse game in which the volatility of ivory pricing is interdependent with outcries by NGOs. When the Chinese ivory prices tripled in 2015 due to increased calls for bans, wildlife NGOs said that the market was out of control and that "there is need for immediate action." There was no change in legislation, and when the Chinese prices fell back to their original level five months later, the same NGOs claimed their work to be going in the right direction.