If you're not going to be overclocking, here's one with an i5-6500, 16GB of DDR4 RAM, and an RX 480:
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-6500 3.2GHz Quad-Core Processor | £174.99 @ Amazon UK |
| Motherboard | MSI B150M PRO-VDH Micro ATX LGA1151 Motherboard | £65.98 @ YoYoTech |
| Memory | Kingston HyperX Fury Black 16GB (2 x 8GB) DDR4-2133 Memory | £66.99 @ Ebuyer |
| Video Card | Sapphire Radeon RX 480 4GB NITRO+ 4G Video Card | £199.99 @ Scan.co.uk |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total | £507.95 | |
| Generated by PCPartPicker 2016-10-01 19:21 BST+0100 |
I'm using a similar motherboard, and similar RAM. I can say they're both pretty solid.
The RX 480 is also a pretty big step up from your R7 370. It should be pretty good as well.
Hopefully your PSU will be able to handle these components. I'm hoping it's atleast reliable, and not on the very cheap end.