How to get work done whilst feeling crippling shame? In academic work, when we are writing or have written a paper for example, there might be strong feelings of shame about the work done or to be done. These feelings can get in the way of finishing or revising the paper, or sending it to colleagues. These feelings may often lead to the writer feeling, quite strongly, suicidal. For example, when shame is the first thing they think of when they wake up. Not getting work done also leads to further feelings of inadequacy and panic over the future. Hence, these feelings make writing difficult, but overcoming these feelings requires finishing the work to a good standard.

As per the title:

How can a researcher write and research when they feel ashamed?

The shame is about the style of writing and the depth of the content/research. It is not about there being something wrong with the research. For example, I might read what I have written and feel too bad to fix it. Or, I might feel that the content (the research) is simply not deep enough, which makes going deeper difficult. Through perseverance, I finish writing papers. But, it takes a long time in an environment where both quantity and quality are important.

I have in the past seen and asked a university psychologist, but they didn't have any specific advice. The psychologist was also supporting too many other members of staff and students to really give enough time to this problem, so I am not sure that this is an option to take again.

I am looking for techniques, founded in psychology, and ideally with some supporting evidence. But more general advice is also welcome.
This sounds a lot like depression, first step is to go see a professional. The fact that you are sharing your experience and identifying what is going wrong is already a good step in the right direction. Share more, don't walk this journey alone. The best I can offer is general advice (things that worked for me). I believe too many people suffer without sharing, so thank you for sharing your story.
What helped me get through it was as follows:

Identify the next exciting thing that you would rather want to start with or do once this is out of the way (a new job, a vacation, a new task, a hobby).
Break down the work into the smallest possible chunks you can (e.g. write a paragraph on X, containing the following points, or improve on X by trying things 1 - 10, or code one six line function).
Then every day, just try to tick one of those off the list. Write one sentence, the next day try to get to two, the next day to three and so on.
The hardest part is to start. Just start. Think of one thing and just type that out, even if it is nonsense and you know it is. You can always come back later and improve on it.
Forget perfection, just get the stuff on the paper and tick off the tasks, see the progress.
Once everything is &quot;done&quot;, critique the work, and write the things that suck about it as recommendations for future work.

Edit:

Forgive yourself every day! What you are going through is a completely valid experience, and you don't have to beat yourself up about it.

The upside of this experience is that you can now more easily identify the next time it pops up and act on it more quickly.
Best of luck. Its not easy but definitely doable even though it does not feel that way.