PhD programs care much more about recommendations than grades. The most important thing you can do is get a good recommendation from a professor at your school who's known to whoever you want to work with at the target school.

As for grades specifically, you can probably just tell them the truth, which is that you screwed up freshman year. Grad school admissions are done by smart people (usually the profs themselves). They'll realize that if you got good grades in the later, harder classes, you could have done well in the easier ones.

Problem is, I can't actually prove I'm doing/have done really well in my final year because it's not over yet therefore I have no transcript. Although they can clearly see I got 4/5 A's in the second year.

Have you worked on any significant projects? Have you done any research? Have you published any papers?

Publishing is somewhat difficult for an undergrad as you can't really get published unless you have something original to say/add to a domain of knowledge (that's the whole point of a PhD). Finding the time to research something original while doing undergrad work is something I didn't even think was possible, the last thing you want is a reputation for trying to publish utter crap.

Because it's rare for undergrads to have research experience, it makes a big difference in grad school admissions. The admissions committee guesses how good a researcher a student will be based on grades, test scores and professor recommendations. If the student has actual research experience, there's less guessing to do.

A lot of professors have smaller projects that are part of their overall research that they can give to undergrads to do.

But, this isn't really helpful to you now. Your question is really "What are my chances?" and I can't tell you. For the people at the top and bottom, grad school admissions is easy to determine. But for those in the middle (I was one of them), it's almost random. Like many things in life, now that I've been through it, I know what I should have done.

If you want to go to grad school, then apply. Not applying is a 100% chance of not getting in. But try looking for schools that do research in what you're interested in, and look at schools outside of the top rankings.

There's no harm in applying. Several students in my PhD program took a year off after undergrad and worked in a university research lab as a paid assistant. Some said that they got into some grad programs after university, but they wanted to get a better research background that would help them get into a more prestigious school.

I suppose it's too late now, but to really distinguish yourself for some top-tier universities, you'll probably have to show evidence that you've pursued research or self-study (e.g. summer programs, indep study/research classes with a professor, personal projects, internships, etc.).

If you are ranked very highly in some key courses, then that would help. Having worked on a substantial project or two could help also.

I think most universities also look at your GRE scores.

From what I've researched it seems universities are only interested in your undergrad or masters degree. High school and college stuff doesn't count (I'm in the UK).

If you are serious about getting into a PhD program then you should have a clear idea of your academic/research goals and some professors you have impressed with your work. Compile professor recommendations, the write up of your goals, and any supporting evidence you have of your abilities: i.e. particularly noteworthy papers, projects, etc.

If you do end up getting rejected, then look around for a project with which to prove yourself. You know what skills you have and how they could be useful. Find another student's project, or a start-up company, or a professor's research which you can contribute to in an important and impressive way. You can use such proofs of your abilities as a ticket into a PhD program next year.