This is untrue. Anyone who has been to school or taught in a school will know that a uniform is unable to conceal socio-economic differences. More affluent families have new uniforms instead of second-hand ones. They replace uniforms when they become dishevelled instead of wearing them until they tear. Poorer students' uniforms are more likely to be poorly-fitted.
Nor can uniforms effectively curb bullying. Bullying in schools, as in wider society, is the result of deep power imbalances that go far beyond what clothes a student is wearing. While uniforms may reduce bullying along lines of clothing, they will do nothing to tackle the root causes of the problem and will merely push the bullying to other avenues of attack and victimisation. 
Most teachers will tell you that bullies will still bully victims even when there is a uniform policy. The nature of the bullying will merely shift to the way the victim styles their hair or does their makeup, or what bag they carry and shoes they wear.