Turbo boost is when the processor needs more power, it'll overclock to a certain speed. That processor is normally maxed out at 1.6 ghz, but can overclock to 2.6
My choice would be either:
ACER Aspire E5-571 15.6" Laptop i3 (1.8 GHz) 6 GB 1 TB £369.99
ACER V5-573 15.6" Laptop i5 (2.6 GHz) 4 GB 1 TB £399.99
For gaming, I'm not sure if 4gb is sufficient enough anymore, unless you're just gonna game and have a couple of programs open.
Someone else may hafta give input
Both have 1TB HHDs, which is great; that'll suit all of your needs
Both have good battery life
The differences are the turbo boost processor paired with 4gb of ram vs. the lesser processor with 6gb of ram
At those low clock speeds, I'm gonna lean towards ACER V5-573 15.6" Laptop i5 (2.6 GHz) 4 GB 1 TB £399.99 because turbo boost may be the bigger difference.
Ask if 4gb of ram is enough. If it is, then that's your choice