If you are going for a humanities grad degree, either scientific or humanities undergrad could get in as long as they get good GRE score (I think.)
Not the case for scientific graduate studies, as the applicant would most likely need to be experienced in lab work and have solid scientific understanding, proven by their undergrad coursework.
Would graduate programs in scientific fields consider a person with no scientific background for even a conditional admission?
Speaking for the US and as someone with undergrad degrees in the humanities who is now doing a PhD in the sciences, it is hard, but not impossible to make the transition.
First of all, your best bet is Masters programs. Unless you're somehow exceptional (or maybe just very well connected), you'd be hard pressed to find a PhD program to take you when you're completely unproven in an area. However, to start out, there are transitional programs out there (Boston University's LEAP program for engineering is one) to help students move into a science field. Ask around and search online; I'm sure there are at least a few others.
You can also take non-degree courses at local universities to build up coursework in your desired field. For those, most schools don't much care about your background as long as you're paying them. Once you've built up enough background/understanding in your field, you may have some luck applying to Masters programs. I've seen other questions on this site where folks have posted schools that accept students to Masters programs in the sciences despite non-science backgrounds. I'll edit this answer if I can find some examples.
Additionally, once you've built some classroom credentials, you may have some luck trying to work with a professor in his/her lab. Even if you're not a matriculated student, I know of at least 2 faculty who have taken on lab assistants from outside the university. It's not common, but it is possible.
In summary, it's possible, but it will take time, probably some money, and some dedication to make the change. You'd probably have trouble getting in anywhere with zero background, but with some patience you can build that background and get your foot in the door. Once you have that, it just depends on how far you want to go with it.
Yes. You have to be realistic, though. Making such a transition takes time, as you're starting from square one. It also can be financially challenging, as you progress through the education. You may not find a lot of choices at first, but with effort, you can begin to expand your horizons after building your academic reputation.
I suppose my answer is from personal experience.
Two years ago, I began to pursue a full, rich career in physics. My undergraduate degrees, though, were in business and psychology. I had virtually no experience outside of introductory collegiate physics and some calculus I had taken as an undergrad. My work experience did not exactly apply.
Not unexpectedly, the choices for a program were limited. I found a good State university nearby that accepted me conditionally to its Master's program. There are some other students at this school who have had other backgrounds as well - another I know well was an English major. Some of us started from scratch. As conditional students, we had to more-or-less complete the entire BS curriculum prior starting grad classes. That took about two years. Where I am now, it'll take about two more years for the Master's.
My partner is in the same boat, but with mathematics. She held a liberal arts degree. She was rejected for conditional admission, and so began to take classes to bolster her foundations. After a year of study, she reapplied and was accepted. Again, she is working towards her graduate degree after several semesters of fulfilling undergraduate level material.
I have observed others in the same situation successfully enter industry and PhD programs at all levels of prestige and interest. Regardless, those who excelled only did so through a lot of blood, sweat, and tears.
So, yes. It's a long road, but it can be traveled.
I don't know of any universities in the UK which would allow this. The reason is simple: in order to complete even basic tasks in science involves knowing the langauge of science (often with a lot of maths).
However, there are 'access courses' in the UK which are 1 year, and have much lower entry requirements. I'm not sure where you are (probably the US?) but I imagine there will be similar things around.
It very much depends on your background - it is possible, for example, to end up with a humanities degree, but having taken a fair bit of math and science as part of an interest, or a liberal arts education.
Fields that don't have a strong undergraduate presence may very well accept you - for example, there are very few students coming in with an undergraduate background in Epidemiology, which means that graduate programs are pretty much expecting to train you from the ground up anyway.
