There is currently no legislation that would allow a group to be designated as a hate group anywhere in Europe. The UK has legislation in place to tackle extremist violent groups under terrorism laws. A group so designated (to which parliament must agree) is proscribed. Membership and support of and for a proscribed group is a criminal offence.
There have been discussions for a number of years now to tackle right wing extremist non-violent groups by designating them as hate groups. They would not be proscribed, but their activities extremely curtailed and related offences were suggested to be civil rather than criminal.
One thinktank defined a hate group thus:
nonviolent extremist groups that demonise specific groups on the basis of their race, religion, gender, nationality or sexuality
Under this proposed definition neither WPUK nor the LGB Alliance would be designated as hate groups.
Anyone who has ever attended their meetings, watched their videos or read their writings would know they do not demonise anyone. They always express the need for equal rights for all groups, including the trans community, and acknowledge that the latter must be protected. They simply adopt a different approach to doing so from those accusing them of being hate groups.
Their insistence that we can protect trans people while upholding women's sex-based rights does not constitute hate and would not see them designated a hate group.