Will it be beneficial for me to pursue a double major in computer science and neuroscience given my interest in general AI and machine learning?

I'd say yes, as a very long-term plan, but having sold into many of the leading UK research schools that cross-over of specialisation tends to come much later, most typically with the Computer Science taking the lead.

By that I mean I've seen fewer people starting with the medical sciences and then getting really deep in the coding side, preferring to partner with specialists who can. But that's very much at the high-end research side. I can't answer to commercial roles.

If you can handle the work rate then a double major would do no harm, since it would show a breadth, and you can then choose which side to focus on after your first degree.

I'd counsel keeping an open mind and not getting too laser-focused at least until you've done your first degree,

I know this question is a few months old. Since the time you asked your question, this field has really exploded. We are using cog sci and ML techniques more and more frequently in my world - AT&T. What I would offer is that we find great value in people with the ability to translate these advanced techniques to the business so we find the most opportunity to make use of AI/ML. When customer need and your field of interest meet, great things can happen! Try to gain some exposure to industry uses and see what piques your interests.