I don’t know whether your Serbian BSc degree is recognized (by means of some EU directives) by the IStructE and you can go straightaway to take the IStructE interview and sit the exam. If your degree is accepted, you should go get a MIStructE or some qualification first. If not, as Andrew suggested, you need an MSc.
In my opinion, an MSc can “show” you got some knowledge about “fancy analysis” or advanced analytical skills (e.g. 2nd order nonlinear analysis) but it doesn’t mean your work experience/practical knowledge shown on your CV is up to a certain level of an experienced and competent engineer. To prove it, taking an interview or exam and challenged by interviewers or an exam.
I am not a job interviewer and don’t know what employers really look for. But a proper qualification looks important in the eye of an employer. Last year, my boss told me he was flooded with a large number of CVs and cover letters. I asked whether you had plenty of good candidates to choose and he said “No, because a lot of them don’t have chartership”. He also said it was a bit weird that engineers with 10 yrs experience not chartered.
Having said that if you want to work in a field which is technically demanding (e.g. design a 2000m long cable stayed bridge or 500m slender tall building), you may a need a postgrad degree.