I've been in correspondence via email with a potential PhD supervisor who has agreed to take me on. After a few emails back and forth and polishing my proposal with his guidance I submitted my application per his instructions. He suggested we interview after I submitted my application. It's been a little over 2 weeks since I submitted. He suggested either a Skype interview or a visit to the campus. Visiting the campus would mean I would have to book some plane tickets. They're relatively cheap since it's within the UK but I'm also on a budget and don't know if I'm going to get accepted or if the interview is required for a decision on my application. I suggested a Skype interview and then during the interview we could arrange a visit on campus but he countered with an offer to just visit the campus during the last week of the month. I was confused so I agreed I could visit campus but asked for him to clarify or provide some guidance on the application process and never heard back from him. I still haven't bought plane tickets and am not sure how to interpret this series of events. Should I just explain my situation to him and ask for a Skype interview? When I agreed on a visit I told him when I would be able to fly out but haven't heard anything so I'm really not sure about buying plane tickets. It all seemed like things were going along smoothly but now I'm very confused. Any suggestions?
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.
A potential PhD supervisor wants me to visit campus for an interview before I know if I'm accepted
You've got things the wrong way around, my friend. It is you who wants to visit with the research group, in the hopes of joining it. It is very much in your interest to go, to get to know these people, to talk to them about their research work and group dynamics, to give some kind of talk... it's not some caprice of your prospective supervisor.
Still, you can and should definitely ask - politely - whether they could offer to cover your travel expenses. Do not insinuate that this will somehow be a condition for your coming to visit.
but I'm also on a budget
After drink, food and lodging, this is probably the next most important thing in the budgeting priorities list. If you don't have money to cover the cost of the trip, and the university/the supervisor don't ofer to cover your costs - take a loan.
I mean it, I'm not joking. Do not give up on this.
... and don't know if I'm going to get accepted
So improve your chances of being accepted by visiting.
PS - All of the above assumes you care about being accepted there. If you just submitted an application as your n'th favorite option then maybe I'd change my answer
I had a similar experience, and personally I accepted. Accepting or proposing an alternative depends on several factors. Personally I accepted because it was a very good lab and it was already a great opportunity to just get a chance at an interview, and because the cost was not crazily expensive and I could afford it (I took the cheapest transportation I could). In the end, it was useful to go there, as I could meet the team and not only the head, so I could see for myself what the ambiance was and get a glimpse of the lab's work and the way they work, and in addition it allowed me to get contacts I could communicate with for further questions, who were very helpful when I had to make the arrangements to set in.
So in the end, I would say that you should ponder the decision. It's not all black and white, it's not an unfair demand your supervisor did, as you can get additional information to make your own decision about joining in (as the team counts a lot!). If you really can't afford the cost or the lab is not a highly demanded one, then you can propose an interview by skype after explaining that your financial situation doesn't afford you to come physically.
A personal visit to the campus significantly reduces the risk that you are making a big mistake by taking the position. Even if there's only a 5% risk of it all going wrong (e.g. because you can't stand the place or the people), incurring some travel expenses to eliminate that risk is well worth the expenditure.
The same applies to the institution as well of course: which is why they might be prepared to cover your costs.
A personal visit achieves far more than a Skype chat. If you go and have lunch with other students, they will tell you things that you won't learn from a formal meeting with your supervisor: for example, what's the best part of town to look for digs.
In this type of scenario, the majority of academic advisors would offer reimbursements for your expenses. I think there is a decent chance that your potential advisor assumes that reimbursement is implied; however, I'm from the US and not entirely sure how things work in England. In my own experience, my advisor is always very busy and tends to overlook logistical matters similar to what you're describing. If your advisor "agreed to take you on" I wouldn't worry too much about acceptance at this point as your admission to the University is pretty much entirely dependent upon that fact. I know you're on a budget; however, you said that you CAN afford it. Thus, you should definitely visit the lab as this is a huge commitment for the next 5 years of your life and it is 100% worth checking out the lab and meeting everyone in person before signing your life to it....even if you aren't reimbursed.
Actual travel would be unreasonable to ask for (but not, perhaps, if it was all taking place within the greater London area). On the other hand, I would consider a skype conversation to be reasonable. You can go into much more depth on specific topics a lot easier than in an exchange of emails.