If I get a bachelors degree without a high school diploma, will I be able to study masters or PHD? I dropped out when I finished grade 11, and started my career as a software developer. I've had a very good experience and working now as a senior software developer.
So, I saw a program in one of the recognized universities in the UK that offers a possibility of admissions to Computer Science bachelor's degrees without high school diploma if there's relevant work experience. So I'm thinking about applying because I actually would like to study more and more and possibly work in a university as a teacher at some point!

So my question, if I got accepted and got my bachelor's degree, will I will be able to apply for a master's degree and then Ph.D., etc? or at some point universities will ask for the high school diploma certificate if I apply to a master's degree or a Ph.D.?

Also, what about getting a job as a teacher in a university after Ph.D.? will that high school thing be a blocker and I'll need to get a high school diploma certificate at some point?
The general philosophy of university and graduate admissions is that your most recent experience counts most heavily. Your secondary school experience is important to getting in to a Bachelors degree program, but, as you note, there are exceptions. 

But if you successfully complete a BA/BS or equivalent you will be considered for graduate school along with any other candidate with the same degree. It would be very unlikely anyone would ask for earlier work. But even if they did, it would be inconsequential compared to your work on the Bachelors. 

There should be absolutely no worries about this issue, provided you do well in the Bachelors work. Your performance there matters, of course.