I have received an unconditional offer from University of London International Programme for distance LL. M. I do want to know whether I will enroll myself on English Bar.

In order to be called at the Bar you need to complete the Bar Professional Training Course; in order to enroll in the BPTC you need a qualifying law degree. As I assume you do not have an English law degree, an LLM will not qualify you to do the BPTC. You would need to do the Graduate Diploma in Law, which is a one year course in which you undertake all of the core modules in order to obtain a qualifying law degree.

PS: If you are a qualified lawyer in your country then, I think, there is a different route.

I hope this helps