You can't buy the R7 2700 for £120 with a free game though, the cheapest you can get it is £134 with the game offer, and that game is now fetching £10 or £12 if you are lucky. The R5 3600 is ~£145-155, so £25-35 more after hoping you sell the game code for at least £10.
I'd say the best bang for buck are the 1600 AF (£85), the R7 2700(£134), and the R5 3600(£155), and each have merits where the others don't.
At £350 to spend on a CPU RAM and Mobo as per the OP's requirements for mainly games, the R5 3600's IPC gain is going to best the rest, but given the use of the GTX 1060 3GB we can only be talking 1080p.
R5 1600 AF with 16GB DDR4 3200 and a mid-level board (£60ish) that takes you to ~£200, use the remaining budget to get a new GPU, and sell the GTX 1060 3GB for £70-90. The £150 left + GTX money, £230ish total you can get a GTX 1660 Super, or for £15 more you can grab the RTX 5600 XT. That will be way better than any of the combinations above, and you'll be able to drop in a better 8-core 4xxx series CPU in a couple of years if you need to.