Sorry to chirp up on the side of the detractors, but you don't seem to be designing this circuit - just throwing cable at it.
What sort of patio lights are you likely to be using ? it may be that 1.5mm cable is more than adequate (eg if you only plan to have a few 10s of watts of LED lighting), in which case you'd use less than half the quantity of (very expensive) copper. On the other hand, if you think you might want a socket there as well then you may need 2.5 or 4mm cable - but you wouldn't be switching it at the house (or at least not in the same way).
Your electrician friend really needs to do the design. Although he may be able to visually inspect the cables etc, he will have to sign a form which basically says "I have designed, installed, and tested this circuit". That doesn't mean he has to have done all the work as he can supervise someone else (ie you) doing some of it, but he certainly cannot truthfully sign that form if he's had no input to the design or installation - hence BASs mention earlier about criminal actions (he'd be falsifying a legal document).
In law, there are only two routes to doing this legally. Either your friend (assuming he is a member of an approved scheme) can do the work and "sign it off" (notify it) himself, or you can notify it via your Local Authority Building Control (at a higher cost !). In theory there is now a legal route to a third party signing off work, but as yet there are no approved schemes, and general consensus amongst the pros here is that there's no incentive for anyone to join such a scheme.
But apart from the legal aspects, you need to be designing the circuits so they a) make sense, and b) are safe and fit for purpose. Ideally you also want to c) avoid unnecessary cost. Guessing what you may or may not want to do in future is another matter - might you need 10mm or even 16mm cable to the garage (you want to run "proper tools" etc), or might 4mm do you (all you need is lights and a socket for the battery charger and/or radio) ? While putting in an oversized cable costs money, it's arguably cheaper than finding you need a larger one later !
What is clear from your questions is that you don't have the knowledge to do this essential design. For the lights, if 2 core 1.5mm SWA is sufficient, then there's a significant cost saving vs 3core 4mm SWA - and it's easier to terminate so you may well save again by not needing extra junction boxes just to terminate the cable.