Breaking into London

Hi guys, i've recently graduated from one of the best university's in South Africa with a 4 year degree majoring in finance. My dream is to be able to work in london and get a FT at a BB/EB, however I am uncertain about a few things and was hoping that someone could give me some advice and possibly answer a couple of questions. (Sorry if they may be repetitive, I've been finding it difficult to find information especially from those who come from African countries).

My main question is whether it is possible for me to break into London and what my best approach is. I graduated with a strong 2:1 (University term ends in December in my country), recently completed my CFA level 1 and am planning to write my GMATs and possibly CFA level 2 during the rest of the year. Would going to a top business school such as LSE/LBS starting next year in 2023 be a viable way to get into IBD in London? I currently have no relevant work experience and am going to try to join a boutique or one of the local banks asap before I do my masters and then try and get a summer directly after and hopefully convert that into a FT offer. One of my main concerns is the visa requirements and whether I will need a sponsor after I complete my masters and also whether this will dramatically impact my chances of securing a summer internship and then FT offer.

If anyone has any advice on what my best course of action should be or any criticisms on my future plan please let me know. Thanks in advance!