While I realize no one wants to "have" to take a gap year, if it wasn't "their choice"/"the plan", it can be really, really awesome and really, really beneficial. It is amazing how much growing you can do in a year, and that alone can make a big difference to your application (for example, how you come across or present yourself at interview, confidence, etc). Besides the chance to focus more exclusively on one area of your application (eg, work experience).
I don't think clearing is likely, but not sure you have 'anything to lose' if you want to try (other than a day of your time). However, be honest with yourself how much will you be getting your hopes up etc? If not getting a positive response on clearing will knock your feet out from under you for a week, I'd say then you DO have something to lose. I admit, while I graduated from a British vet school I was a foreign applicant so I am not as familiar with clearing as other posters likely are.
Did you get an interview? Did you get any recommendations on how you could improve your application to be more competitive? Do you have all the core placements (sounds like you are having trouble with farm but do you have any farm at all?) and the "minimum" recommended number of weeks? What about your personal statement, any feedback there? Do you do Duke of Edinburgh, or have any long-term hobbies outside of school/your vet app that you can talk about, maybe use to show time management etc.? I agree that 'longer term' placements COULD help you there.
I can't remember if I mentioned this in this thread already so apologies if I did but in addition to newspapers etc. I would recommend online classifieds, social media and so on eg Yelp, gumtree, etc. as ways to advertise for placements.
I did the GEP program, as did most of my close friends, so we wouldn't have been eligible for financial aid, regardless. However, from talking to others there was still a fair bit of competition for scholarships, grants, etc. I agree you have a better chance at being eligible than a lot of people, but not sure there are enough to 'go around'. Silverstar likely knows better than I do though; and may depend on the uni.
Off topic, but I notice you mention not caring/it not bothering you/something like that as regards to working as a kennel assistant and being involved in euthanasias. I respectfully suggest you NOT SAY THAT, nor post it publicly, for fear it could be taken the wrong way (eg compassion fatigue or burnout).