I'd likely be looking for a B450/R5-2600X combo, and a 16 GB /3200 MHz RAM kit (2 x 8 GB)....that will eliminate any cpu-limitations...(If an Intel fan, the 9700K and Z390 are the desired rage these days, but, that combo , plus a cooler, will likely add $300-$350 to the build, including the cooler)
The GTX960 is going to be challenged in some modern games at even 1080P/high quality, but, see if you are still content with most games at 1080P/medium settings...(For sure, your cpu is a large limitation right now , though, and, upgrading it demands a new MB and RAM...; that should run about $500 or so USA prices, might need to add $150 for the VAT if UK prices/parts sources....)
WHen you have another $280 to spend, the GTX1060Ti is coming, with GTX1070-rivaling frame rates...
Good luck with the build....