Dr. Gautham's Reply:
First of all you have to decide what you want. You must prioritize.
Do you want a career in medicine or a marriage first? If you decide that it is a career in medicine that get preference, your marriage can wait. In such a case, you can wait for him to convince his father to consent for the marriage, and then get married.
If you decide that marriage takes precedence, you must be willing to let your career take a back seat. In such a situation you then have to figure out why his father is against the match when the horoscope match was initially confirmed by his parents. The horoscope mismatch appears just to be an excuse and you have to find out the real reason why his father is against the marriage now.
It is important that you convince his father before you get married because he values his family. You are right about the importance of social relationships post-marriage.
I would not recommend going into the marriage against his family. Remember, if you are both strong, no one can force either of you to marry someone else. But, you have to be willing to wait. And once his father sees that he is seriously intent on marrying you, I am sure that he will turn around, unless he is an unreasonable man who does not care for his son's feelings.
Under the circumstances the best bet would be for you to plan to take the PLAB test and get a job in UK. You will then be nearer to your fiance, your relationship will strengthen, and it will show his father that you are serious about joining his son. It will also take the tedium out of the wait. Then, when he is able to convince his father, you can get married. I am sure that you will find that it was well worth the wait. Let me know how it turns out.