As a citizen of the United Kingdom, you can stay up in Serbia to 90 days without a visa, the only condition that you have to fulfill is the possession of a valid travel document. After the expiry of that period, there is a possibility to apply for a visa type D (temporary resident visa), which can be issued on the basis of:
1) labor, employment, performance of economic or other professional activities;
2) education, studying or training, scientific research, practical training, participation in programs of international exchange students or students or other scientific and educational activities;
3) family reunification;
4) other justifiable reasons in accordance with the law or international agreement.
Applying for a visa type D, includes sufficient funds to cover the stay and the compulsory health insurance, in case you need medical services.
I hope it has been helpful