I am looking to pursue a Master's in International Relations in the UK.

Would it prejudice my application in any way if my Letter of Recommendation, as sent by my referee from his Institutional Email ID and written on the Institutional letterhead is not signed?

Please help me out. Worried.

No, I don't think so. They know it is from him since he has emailed it. As far as I recall neither of my references were signed. I don't think it will do any harm as long as it was not a specific requirement. If you feel really bad then just contact the admin team and check. And if they say a signature is needed, go back to your referee and request one.
Good luck.