Quick update - been in the UK for one month.
Below are some consolidated tips and tricks for anyone interested:
Banking: Start off with Monzo once you get a BRP - quick and easy.
For more "traditional" banking Lloyds were the quickest to help me as a South African. Some companies ask for proof of addresses and thus Lloyds will be better positioned for this if you apply for more services etc.
Drivers licence: I swopped my SA drivers for a British licence. It cost about £50. All you do is go to a local post office and ask them for the forms. All instructions are on the form. You have to submit your BRP in the mail as a form of ID and having dealt with SAPO all my life, this felt dodgy AF. Initial turn around time as per the form was 5-6 weeks. I got my BRP back and my British licence in 10 days flat. A drivers can be used for proof of address too when signing up for services etc. Also you seem to pay less on car insurance if you have a local licence.
Interweb: Uswitch.com as per this thread. I didnt have any deals in my area that qualified for vouchers etc, but my inner bargain hunting South African simply asked and I was promptly given a £50 credit on my account and a £100 shopping voucher.
Cellphone: I also signed up with Smarty via Uswitch. It lowers the months cost from £18 to £16. Then I referred my SO and we both got £10 Amazon vouchers. Its truly uncapped. No throttling, no shaping. Most I did was 40gb in a day using my phone as a hotspot to stream Netflix in HD. In all honesty hot-spotting will suffice for most people and you dont really need "extra" broadband
HMRC services: I applied for an NI number, NHS, and to be on the electoral roll via the gov.co.uk website. This is either done instantly or takes a few days at most.
Shopping: I arrived with minimal stuff (my container arrives next month apparently) and simply used Amazon (signed up for a free prime trail and then canceled before getting charged). Word of caution. Amazon might be fast, but its not the cheapest. I track finances down to the penny and found loads of beter deals via Ebay, Ikea, Wayfair, even Saintsburys for household goods. Shop around.
Insurance: I used
https://www.moneysupermarket.com/ then simply go directly to the cheapest provider for a further discount, if needed. In my case Marshmallow was the cheapest for car insurance, then I went straight to them and saved a further £15pm for the same coverage.
Commuting: Fok, this was a real pain in the butthole. I initially walked everywhere and took trains & busses. As someone that drove everywhere prior this was a big adjustment (for the better). Then I got fed-up and bought a POS Bicycle off Gumtree for £30. Public transport is amazing - I cant fault it, but for somethings you do need a car. Weekend away, traveling to areas where bus routes dont go, grocery shopping etc. Im in a position now that I want to ditch the £30 bike and get something decent, Ill still cycle to work (weather permitting).
If you dont have a prior credit record in the UK you can forget about getting financing for a car. I tried everywhere. I was fortunate enough that my SO has had a local HSBC bank account and this gave her somewhat of a "credit" record. We had to jump through a lot of loopholes to prove that we are credit worthy (inc submitting docs from SA) in the end we got pre-approval for a loan at 8.9%. Not great, but not too kak considering the circumstance.
I can write a book on what car to buy, basically just get an electric. Taxes, petrol & diesel and congestion charges are on the up for traditional cars. There are charging stations everywhere and the UK is small. Its a no brainer.