Applying to a full time lecturer post in the UK in a psychology related field I am a non-European applying from outside of the UK. I need to come up with realistic external funding ideas for the next three years. I have a good idea of what kind of research I would like to do but there is no definite plan. Any resources to consider for funding are greatly appreciated.
I'm from a physical science field in the UK, so things could vary in different faculties.
From my experience, new faculty at research intensive UK universities are usually required to apply for a New Investigator Grant during their first 3 years as part of their probation. Hiring committees will therefore be looking to see that you have plans which have a realistic chance of winning such an award. It's important that your plans for this award have an appropriate scope. You can find information about the ESRC New Investigator Grant here: https://www.ukri.org/opportunity/esrc-new-investigator-grant/
That is probably the most important one to mention. But mentioning other plausible pathways to funding is also helpful. Depending on exactly what your research interests are, a few other popular UK funders which may be relevant are:

Wellcome Trust
Leverhulme Trust
Royal Society

If you have experience with EU grants such as Horizon Europe (which the UK remains a part of despite brexit), this would be worth mentioning. But I get the impression applying for such grants is not common/expected from junior academics. If you are working in Clinical psychology then you would probably need to look for more medical related funding, in particular through the MRC, which I am not very familiar with.
UK academia is very interested in the impact of research due to the Research Excellence Framework. If you can show how your research has/does/will generate impact this will be to your advantage.