Is my computer good enough for gaming?

I keep on lagging…

Specs:
Operating System: Windows 10 Pro 32-bit
System Manufacturer: LENOVO
Processor: Intel(R) Core(TM) i5 CPU M 560 @ 2.67GHz (4 CPUs), ~2.7GHz
Memory: 4096MB RAM
Available OS Memory: 2996MB RAM
Microsoft Graphics Hybrid: Not Supported

What cheap (£300 or lower) but quality gaming system do you recommend?
Thanks!

Added (1). I found this Zoostorm Tempest Gaming Desktop for 250. Http://www.ebuyer.com/719683-zoostorm-tempest-gaming-desktop-pc-7260-5099

Specs:
rocessor
AMD A6 6400K 3.90 GHz Dual Core
Cache: 1MB
Memory
4GB DDR3 1600Mhz RAM
Supports up to 16GB
2 x DIMM sockets (1 used)
Hard Drive
1TB SATA HDD
Optical Drive
DVDRW
Software
Windows 10 Home
Chipset
AMD A55M Chipset
Display
N/A
Graphics
AMD Radeon HD8470D - on board the CPU
Audio
High Definition Audio, 7.1 channel

Without a video card no it won't even run games period.

also didn't even know they made 32 bit win 10