First of all, to answer your specific questions:
Depression is a mental health issue, and I'm going to claim that's self-evident. What's not self-evident and more relevant is whether it's a mental disability. I'll discuss that below.
You are never obligated to disclose any health issue unless it affects your ability to do the job. As you describe it, that clearly isn't the case here, since you've maintained your grades and had good performance reviews in your internships.
To expand somewhat:
There are firm definitions in the UK of what constitutes a disability with regard to employment law: it's something that has both a "substantial" and "long term" negative effect (Source: Gov.UK).
In general, I would expect mild-to-moderate depression not to count. I expect severe depression lasting (or expected to last) more than 12 months would count. (For foreigners, I'm using the UK definitions of these terms based on my experience with my own diagnoses; I have no idea if they mean the same or are used at all elsewhere.) You'd need to speak with your GP to get a more firm idea of whether your present or past depression counts as a disability, but based on your description (specifically, it being "various occasions" rather than a chronic condition, and your maintaining good grades and positive performance reviews), I suspect not.
If you disclose any disability to an employer in the UK, the Equality Act 2010 etc mean they are obligated not to unfairly discriminate against you and to make reasonable adaptions for you ("unfair" and "reasonable" preclude someone who needs a wheelchair to move about from working as a paramedic, for example). However, unless a disability affects the job you're doing, there is no requirement to disclose it at any point. (Source: Prospects)
In any case, I'm surprised a recent job application has asked that question. Under the Equality Act, an employer isn't allowed to ask about health or disabilities at all before they offer you a job, except with the specific goal of making accommodations for your application (ensuring there's a ramp in place for someone in a wheelchair interviewing, for example). (Source: Time to Change and ITD)
For further reading, take a look at Time to Change. It's a website and campaign run by the charities Mind and Rethink Mental Illness, and funded by the Department of Health, with the goal of reducing and removing discrimination based on mental health and mental disabilities. Their Support in the Workplace section is obviously particularly relevant.