How do i get a multiple entry Uk visa so that I can visit the Uk more often on my trips to the rest of Europe?
All "Standard Visitor Visas" are multiple entry by default. You can come and go multiple times. Of course you have a landing interview upon arrival where you state your premise.
I would not like to apply for a UK visa each time I go to the Uk and London, is this possible like I did with the Schengen visa?
The visa is issued for 6 months. They will not issue a 2 or 5 year visa until you have lots of experience with the 6 month visa and they classify you as a bona fide visitor. Also, you need a strong premise to get the 2 or 5 year visitor visa, it cannot be just a matter of personal convenience.
Having a Schengen visa is of negligible value to the UK. Schengen is not officially recognized by the government (except for agreements to share information).
To apply for a Standard Visitor Visa, you can open an account at Visa4UK and fill out the application. Based on everything you wrote, your first screen should look be filled out like this...
It is emphatically recommended to study the rules and guidance before setting out. The visitor rules are in Appendix V. We see a lot of refusal cases here that could have been avoided by reading the guidance.
The carrier will not allow a South African to board unless their passport has an entry clearance in it. It prevents their being fined (and prevents you from being served with a removal notice). The experience of a boarding refusal gets people upset because of the distress of wasted time and airfares, so it should be avoided by having the right visas. There are some articles on this site where angry people wanted to blame the carrier for selling them a ticket in the first instance, they may be worth reading. The bottom line is that it's spelled out in the small print of the ticket's terms and conditions that you are responsible.