For Serbia your UK residence permit /visa is sufficient to enter, as well as a schengen visa or a residence permit or of any other EU member state as well as the U.S.A.
http://www.mfa.gov.rs/en/consular-affai ... isa-regime
At its meeting of 30 October 2014, the Government of the Republic of Serbia adopted the Decision on visa free entry to the Republic of Serbia for holders of foreign passports having a valid Schengen, UK and other Member States' visa, or visa of the United States of America, and for holders of foreign passports having residence permit in the countries of the Schengen area, EU or the United States of America, which was published in the "Official Gazette of RS", No. 119 of 31 October 2014 and which will enter into force on 8 November 2014.
By this decision, the above-mentioned categories of foreign nationals may, without prior visa application, enter, transit or stay in the Republic of Serbia up to 90 days during a six-month period, but not exceeding the expiring date of the said visas or residence permits.
There is a possibility for foreign nationals to enter the Republic of Serbia with two passports e.a. expired national passport with valid visa or residence permit and valid national passport without valid visa or residence permit.
Foreign nationals, holders of a residence permit in the form of a separate card (not a sticker affixed to their passport), must present their valid passport, upon entering the territory of the Republic of Serbia.