score:4
Converting comment to answer for the Answerathon...
It will not be refused on that basis alone, and as long as you have returnability to your home country, then it's fine.
This answer relies on Paragraph 28 of the Immigration Rules, which says in part...
...An application for an entry clearance as a visitor or as a short-term student must be made to any post designated by the Secretary of State to accept such applications...
...and there is a British mission in Dublin designated by the Secretary of State to accept entry clearance applications.
And for completeness sake we also look at Appendix V of the same rules, which states in part...
Applications are decided based on the information provided by the applicant and any other relevant circumstances at the date of decision.
and also...
(d) provide a valid travel document. Where the online application process is not available, the applicant must follow the instructions provided by the local visa post or application centre on how to make an application.
...a travel document is a passport in your case. They are not immediately concerned about what's inside the passport in terms of expiry dates of visas.