would this make you angry?

I had this exact same problem. I worked in a really busy office with 15 other people in a relatively small space. When I told my manager that I was finding the office environment too overwhelming and was giving me sensory overload she told me to 'adapt my working style'- by that she meant find a quiet room to work in. Which is impossible in my building and my point was, what's the point in having an office if I can't work in it? I'm now in a smaller office with 4 other people and that's only because someone in that office has left and so that freed up space for me to move. 

I'm now finding things easier, but that whole period was very stressful. I'm having my autism assessment in January (so nervous) so until I have a formal diagnosis, it's difficult for me to actually ask for reasonable adjustments. 

My advice in your situation is to try and find a solution for yourself, and then present them with your solution. Rather than just kind of saying, I need to move where do you think I should go? Try to present them with a solution I,e I could move to so and so room as it's free etc. I find workplaces seem to be a lot more open to helping if you offer them suggestions of specifically what you want.

I hope things get sorted for you soon as I'm sure it's causing you stress and sorry I couldn't offer you more helpful advice!

There has been subtle bullying, i.e. exclusion, i.e. they don't want to include me in their social activities - coffee morning, lunch, pub quiz etc, and also at a work level - I am not kept up to date with what's going on in the lab, or invited to participate in practical work, despite my repeated offers to help out with lab work etc. As a result, I'm being prevented from learning techniques necessary to facilitate my PhD.

I regret not recording any of these instances (e.g. ignoring me to my face, making social plans when I am in the same space), much of it has been flat out humiliating, but to be honest I've been so overwhelmed by trying to keep on top of my PhD work that I simply don't feel I've had the time. If my diagnosis had come before I joined the group, I think I could have used my new knowledge about ASD to protect myself from such events, but unfortunately it is too late now.  

It's difficult to know how much of it is caused by my perceived aloofness. I think generally over time they've created negative assumptions about who I am as a person. I don't want to tell them that I'm autistic, as I don't trust them or understand fully what the consequences would be on my career. I feel my best bet is to muddle on by myself, and try and at least improve the quality of my working environment (e.g. by reducing noise etc). But it's hard doing a PhD without any moral support. Especially as I've been going through a serious depression since I've been here. 

Although I'm not working at the moment, I spent most of the last thirty years working in open plan offices. When I needed to avoid distractions, I just used to listen to music, which generally helps me concentrate better anyway. Sadly, only high level managers seem to get their own office nowadays.

Universities don't have a lot of desk space in general, so it might be that they genuinely can't find you anywhere else. They can only provide you with a quiet space if they actually have the space, they can't magic up an extra desk if there isn't one. We've recently had a new building, but it still didn't actually add any more capacity, as soon as we'd moved in everything in the department was full again.

Could you scout out potential places to work for yourself? There might be somewhere you can informally make your working space (for example one of our computer labs is open to anyone for research, and occasionally small groups of undergrads are allowed to work in there, but in practice, another student in my research group has it to himself 90% of the time), or asking round the academics and people in your building might give you some ideas where there is desk space free. The 'relevant people' might only know is free on paper, whilst in practical terms there might actually be other spare desks that people don't use, or people who might be willing to swap if only you ask.

Failing that, is there anything else that might work to make your working environment more tolerable? Noise cancelling headphones? Could they set up some barriers so you've got a little cubicle round your desk? Move your desk to at least another part of the room?

Sounds like a question for a union? So that you know your rights?

Maybe the other building isn't too bad, like @Zomted said. As far as I know from experience, universities don't have a lot of spare space for employees, so it might be the best they can do.

It might be too much to ask to AND be with your team AND be by yourself. Like the cake and the eating thing. Depending in the spacing situation.

I hate open plan Soooo much!

as far as desk goes its tricky, depends on what they (and you)decide is a reasonable adjustment. Id suggest having a look round the institute yourself to see if you can find somewhere you could have your desk then ask for it. Itd be much less easy for them to refuse that. If the whole place is open plan though it may be trickier.

What about the other building? Is it far and have you seen it. If its really nice and not too far maybe it would be OK. You wouldnt get disturbed by your colleagues at any rate. If though its miles away or you need to regularly trek between lab and desk, clearly thats no good.

what else has been going on? Keep a record. Most unis have bullying and harrassment procedures and its not on if thats happening to you.