i plan to do the university of london external LLB and top it up with an LLM from UK. Would the LLM deem me eligible to be called to the Bar in the UK? Would I need further education to be called to the bar?

Yes. Your LLB would qualify you to take the BPTC (bar vocational course), provided you have taken all the uk required core law modules and obtained at least a second lower. LLM is irrelevant in bar admission, it doesn't help, unlike the US