I have finally managed to solve the issue.
It looks like I did not upgrade the WebAPI project correctly.
The line below was missing from my WebApi Module's Initialize() method:
Configuration.Modules.AbpWebApi().HttpConfiguration.Filters.Add(new HostAuthenticationFilter("Bearer"));
Once added, the 401 response code is returned.
ABP version is 1.2.2.0
I've made the request, bit it returns with a 200 OK code and the body of the response is the login page HTML.
It must be noted that this is not an ABP Core project and that it was upgraded from ABP 0.8 to 0.11 previously and then upgraded to 1.2.2 yesterday.