What is the most affordable way for small capital retail investors to invest in the London stock exchange? Which platform would be good?

For LSE, your options are limited. Most commonly recommended are Standard Chartered and Interactive Brokers.

Standard Chartered has higher forex spreads and commission as compared to Interactive Brokers. However, Interactive Brokers charges $10 minimum commission monthly if your AUM is below 100k USD, which can add up if you are a smaller investor.

There's Saxo but their 0.75% currency conversion fee and 8GBP minimum commission makes it hard to recommend.

Yes, for me (not a customer) Standard Chartered seems very o.k.

can be expected nicely the investing universe of the mainstream SG broker to expand and the fees generally to drop in the near future

to circumvent the higher SC forex fees you could send/convert SGD to EUR into your Standard Chartered account (maybe some brokers, as Saxo, refute these transfers? Then you could circumvent it by sending EUR after TransferWise flipping into your own multi currency EUR account and send it afterwards to Standard Chartered.)​​​