I am an Indian passport holder and I have an italian residence permit card which is going to be expire on the 25th of September. No doubt I am going to renew my documents but I want to visit the UK for few a days in this July. Can I apply for a visa with validation of 3 months or less of residence permit card?
UK Immigration Rules do not specify a minimum validity period for residence permits. The eligibility requirement is to be able to show ties to your country of residence that demonstrate you have a compelling reason to leave at the end of your planned visit eg job, family, savings.
So yes, you can apply.