Universities offering PHD in Economics or CS without requiring a masters degree
Generally you can get a place for a Ph.D. in the UK or US after your Bs.c.; however it is a time consuming process.

For this I would suggest the following steps:


Ask one of your lecturers about this. They might give you recommendations based on their knowledge. For example if you want to do a Ph.D. in E-commerce try to ask this from a lecturer who teaches this.
Ask your personal student advisor or your last year supervisor. You need their recommendation letter more than anything to get a Ph.D. position besides your marks.
Look for lecturers in the top 50 universities yourself, and try to communicate with them through your university email.
Repeat till you get there! It might take up to a year to find a place; so meanwhile you could get a job so there will be no gap year in your CV.