I've only skimmed this thread, so much of this may already have been said.
You don't need a prototype, though it may not be a bad idea. You do need a drawing and/or description sufficiently detailed that the product/process can be made from that drawing/description.
You can only patent products/processes that are innovative, not inherent in the existing body of knowledge and are capable of industrial/commercial exploitation. Ideas don't qualify, though some other forms of protection (such as copyright and design rights) exist to protect other forms of IP.
Cost? Not trivial. It depends on the extent of the coverage. You can. as I understand it, do much of the research yourself, but using a patent agent (a good one) makes sense, firstly to ensure that the patent application is done properly and should not be able to be challenged, but also to do the necessary research prior to filing. If the process (or whatever it is) already exists as part of public knowledge (and I mean worldwide), then any application will either fail, or will be nullified if challenged and that prior existence demonstrated. So, careful research is essential to avoid wasting the cost of a full application.
Next .... do you want protection in the UK only, or worldwide? If the latter, you'll need to go through the process in a large number of countries.
Also, fees are ongoing. So, you don't just make one payment up-front, and that's it. Unless you actually intend to seriously either develop and market real product based on this idea, I'd forget patents. Alternatively, get the patent and then grant licensing rights .... IF you can find anyone willing to pay you for them.
Or, you could hold discussions with manufacturers based on non-disclosure agreements, but if you do, then :-
1) Get a lawyer to draw up the agreement to be sure it's as watertight as possible.
2) Be aware that a manufacturer, once aware of your basic concept, may be able to come up with an improvement or variation that would be outside the scope of an NDA, because no manufacturer is going to sign an NDA so broad as to limit their own independent creativity. It would be commercially stupid to do so, based on an unknown entity such as a student’s idea. If you had a successful track record, that may be different. Moreover, you'll have a job getting any significant manufacturer to even meet with you, let alone sign an agreement. You'll find you're the supplicant, not them. You need them more than they need you.
And actual cost? One recent study showed that a decent patent would cost of the order of £75,000 to obtain and maintain, over a period of something like 7 years. But, bear in mind, the cost is NOT fixed. If you get a legal challenge on your application (and even a patent grant can be challenged), you either have to cave in, or be prepared to stump up quite large sums to defend it. So that £75,000 will be much higher than some patents, and much less than others (especially if subject to a protracted legal fight).
You can pretty much guarantee that it's going o cost you several thousand pounds over a few years, if you do it properly, as a minimum. So, as I said, unless you are either loaded and have money to burn, or really think you're on to something that is feasible, marketable and commercially viable, and are prepared to seriously follow it through, forget about patenting it.
