Unless you intend to overclock just get a cheaper motherboard and a faster CPU such as Core i3 2100. Even OEM Core i5 CPUs can be had for under £120 if you shop around.
The Gigabyte GA-H61M-D2H-USB3 can be had for under £50 and is an H61 based mATX motherboard which has 4 RAM slots.
A G850 is a false economy IMHO,as a Core i3 2100 will have a longer lifespan IMHO. Newer game engines are starting to utilise more threads now and the HT of the Core i3 2100 will be useful in the longterm.
Edit!!
Also a Pentium G620 has almost the same performance as a Pentium G850 for a much lower price too.
That is a good point, as you mention it all depends on whether the OP really wants to upgrade his CPU and overclock in the future. But as you say, you are basically trading off performance now for overclockability later by going down the pentium/Z77 route.
At the moment you can get a low end (but still perfectly functional and ivy bridge supporting)
H61 motherboard for £36. Add in £30 for 8GB of RAM (the kingston kit is great) and that leaves £114 of the £180 budget for a CPU. For this price you could get a i3 or even a second-hand i5 (like the 2300 or 2400). If the OP is willing to spend ~£20 more then he could even afford a brand new i5 2300.
This option would give you much more CPU performance now and in the case of the i5 - twice as many cores and the benefit of turbo boost.
This chart compares the performance of a Pentium G850 and an i5 2400 in a range of tasks.
The H61 boards don't support overclocking and don't have the nice features of Z68 or Z77 boards (like many PCIE slots, SATA3 and USB3), but they fully support all LGA1155 CPUs and are cheap to buy.