According to this article by Nicola Davidson, posted to CNN, there is an ongoing effort in the UK to institute a "near-complete ban" on ivory similar to the ban put in place in the US. From the article, it is unclear if the UK ban would only pertain to elephant ivory or would include walrus and other sources exempted by the US ban.
http://www.cnn.com/2017/04/12/luxury/antique-ivory-debate-uk/index.html
Information on the US Ivory ban can be found here.