Is the R80-150k you are referring to the amount needed to fund the moving portion of emigrating, the paperwork/flights/shipping to get you and your belongings legally into a foreign country?
For one person I would say you need around R200k to emigrate to the UK. It does depend a lot on how long you will be out of work when landing, and whether you have a place to stay when you land (in other words, that won't cost you anything).
I started working one month after arriving, and stayed with family friends for 3 months, and I still needed around R200k. Granted, I did spend a lot of money on furnishing a house. So if you rent a furnished house, you could probably get away with R150k.
The visa itself is around R8k, national insurance will cost you R40k (once off), you need a TB test (R1800), the flight, and money to last you until you get your first paycheck (often 2 months). Then it is helpful to have enough money for a deposit on a place to stay, which is around 6 weeks rent. Note that it is 6 weeks rent assuming you have found a job already. If you haven't found a job, it would be much more - if they would even rent to you at all.