I am a resident of India and I moved to Italy 3 weeks ago for my PhD. I have to visit the UK in the last week of November for which I'll need Italian residence permit for my visa application. I have already applied for my residence permit, but it will take another couple of months to receive (I might get it in December). Therefore, Italian police headquarters has agreed to give me a temporary residence permit which is valid for 3 months. Is it possible to apply for UK visa using the temporary residence permit?
According to UkImmigrationSpecialist:
If you are applying in the country of which you are a citizen, you can submit applications in any UK visa category. If you are not; the following rules apply:
Applications for transit visas, visit visas, and EEA Family Permits may be submitted in any country offering a UK Entry Clearance (=visa) service.
So the answer is: yes, you may submit your application in Italy without having a regular residency permit. It would even be possible on a tourist visa, assuming you had enough time to wait for the processing.