DON'T DO THIS WORK. I don't wish to be rude but you clearly don't know how to do this safely.
Firstly you are suggesting not using switches for the two new lights - INCREDIBLY DANGEROUS. All lamps must have a switch to isolate supply for maintenance e.g. changing a bulb!
Secondly you haven't assessed the load on the lighting radial and whether it will take the new lamps. You haven't identified the type of wiring needed (1mm2 minimum, ideally 1.5mm2).
Secondly from your diagram you are proposing to use the old style connection boxes - these are against 17th ed regulations and you have to use maintenance free terminal boxes or ensure all cables are clipped securely and are accessible for inspection and maintenance.
You have no way to perform an insulation test as you don't have the tools and you have no way to ensure that earthing resistances and loop resistances are correct and have no way to test the RCD function- as you are extending to external fittings you would need to ensure the lighting radial is RCD protected.
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