A potential PhD supervisor wants me to visit campus for an interview before I know if I'm accepted
The solution here is honesty and candor. You should explain that you would like to visit the campus, but that your financial situation doesn't allow it at the moment. Any reasonable person would either drop the suggestion of a campus visit, or find some money to pay for your travel expenses. Any other reaction would be a red flag.
I recently traveled across the UK by train for two separate interviews (from St Andrews down to Norwich on one occasion, and down to Oxford for another), so I can from personal experience say that situations involving traveling for interviews seem relatively common.
In both instances, reimbursements for travel expenses were a given, and involved submitting the tickets and a summary of the costs to the university after the interview. In one of the instances I had to email the university and ask about reimbursements, while in the other it was stated ahead of the journey that travel expenses would be covered.
Based on this, I would highly recommend asking them whether or not travel reimbursements are available, or, if the cost of buying tickets cannot be covered by your budget until the time that the university sends you the money, ask whether the purchasing of the tickets can be paid for by them ahead of time. In situations like this, it is often best to be specific and make sure that the university knows exactly what is required of them.
Several other alternatives also remain. As suggested in another answer, coaches are often cheaper than flights, in addition to being readily available, and train tickets can often (as far as I have heard; I have not tried this myself) be purchased by a third party on behalf of another traveler, allowing for the university to pay for the tickets ahead of time.
Assuming you want to go to that university and work with the advisor, I would say the cost of a domestic plane ticket is probably worth it given the impact on the next 4 or 5 years of your life.