Assuming you stick to your £100 - £130 per monitor you'll have between £90 and £150 to play with.
Pushing the upper end of that range will nab you a basic GeForce 950 or a Radeon 380 with 2Gb of onboard memory. If you have intentions of playing games I wouldn't drop lower than that tbh. Either of those will happily drive two full HD displays and gaming at decent frame rates on one display shouldn't present a problem. Not sure how they would cope trying dual screen gaming but I suspect frame rate would be borderline unless you cut back on the quality settings. Would depend on the game of course.

If you can stretch to £200 territory for the graphics card your into GeForce 960 or Radeon 380X territory and 4Gb of card memory which will give a decent step up in performance and make dual screen gaming a more realistic option.

In the end it really depends on how much gaming (and what sort of games) you want to play and whether you want to play on both screens at the same time.
The cheaper cards will be more than sufficient for coding and office type use (the CPUs onboard graphics would cope with that sort of use these days without an issue).

tbh the gaming would only be race games, rather than anything else, most of the time would be web, office coding.

I imagine that racing games place similar demands on a graphics card to FPS ones as you're trying to rapidly render scenery and stuff. Provided you stick to a single monitor a 950/380 should be more than sufficient at FullHD resolution and overkill for your normal, non-gaming usage.
Having a quick scout around various reviews shows the GeForce 950 managing around 50 - 70 fps in Grand Theft Auto V at 1080P (which is the closest to a racing game the reviews seem to get) and broadly similar in a number of FPS games. It does seem to struggle with big simulations (Rome Total War sort of thing) where it drops into borderline juddery territory (under 30 fps).

My work PC (Core i5-4570) quite happily runs dual 1080P displays for office type work although I can't comment on gaming performance.

My PC, (Core i7 6700 - Skylake) has a GTX760 and I can happily play the new Star Wars game on the 4K monitor, at 3840 x 2160, if that's any help.

Interesting, I wouldn't necessarily expect that. Still, performance can vary wildly from game to game depending on optimisations.

As if by some spooky coincidence the Hexus review of the new GeForce 1060 may be of interest:
Linky

They've included a number of older graphics cards (including the 760 as it happens), and they've used Dirt Rally as one of the test games. The link above starts at page 4 of the review (where they actually start doing some measurements), the Dirst Rally stuff is on page 5. Playable frame rates pretty much across the board at 1080P, including from the GeForce 760.

that makes interesting reading.. thanks

looks like either my memory or motherboard has taken a dive. If it's the motherboard is it worth replacing it or would it be more prudent to buy a new pc? it's about 4 years old....

Depends on the spec you'd want obviously, but four years is about a fair lifespan for a PC IMO.

At 4 years old, you're almost certainly looking at the new motherboard not supporting the same CPU and RAM as you currently have unless you can actually find a 4 year old motherboard to replace it with...

the MB is one of these..

P8Z77-V LX Intel Z77 (Socket 1155) DDR3 Motherboard

had a quick look and it will be around £130 to replace.

I am now wondering whether a new box would make more sense in the long run...

Depending on what your current box is and whether you are happy digging around inside, you can probably do a MB, CPU and RAM upgrade and leave everything else the same. Will get you a vastly quicker machine without the expenditure of a full new unit.

There is plenty of space in the box as it is a full tower with plenty of bays, looks to be plenty of cooling. The pw is 520w. Graphics card is xfx 7850 so I think that could stay.

I am not sure what to buy though, mb, cpu, mem these days...as to whether I could plum it all together....that could be interesting. ?..

If in doubt, have a look at a motherboard bundle:

https://www.scan.co.uk/shop/computer-ha ... rd-bundles

I'm pretty out of the loop on PC hardware these days, but I'm sure others can pitch in on the sweet spots of the current CPU lineup.

As for monitors and graphics cards it very much depends on intended use and budget.
From previous info in the thread it doesn't sound like you need a large number of cpu cores. I'm not overly familiar with AMDs CPU offerings but I get general impression Intel has them comprehensively beaten out of the bottom end of the market. The only area I think they do relatively well is with their integrated gpu but your xfx 7850 is probably superior to any igpu anyway.

If you go for Intel and can stretch to it a motherboard based on the Z170 chipset gives you maximum flexibility. Likewise I'd say the i5 range gives you 4 physical cores and a decent turn of speed. Going from jons link you can get a pretty decent Z170/i5 bundle for around £300 although that doesn't include RAM so you'd be looking at another £40 - £60 depending on speed and capacity.

If that's too expensive then the H170 chipset is broadly similar to the Z170 but drops features like overclocking support, the ability to share PCIe bandwidth between multiple graphics cards and it drops a few USB ports as well. If you weren't planning on overclocking and were going to stick with a single graphics card that's no great loss and mobos can be picked up for as low as £70 (for ATX form factor). At the bottom you get the H110 chipset which starts around £50 for an ATX motherboard although it drops a number of features to get there.

You could put together a H110/Core i3 system with 8GB of RAM for under £200 using your existing components whereas adding £100 - £150 to that gets you a much more powerful and upgradeable Z170/Core i5 system.

The current processor is either an i5 or i7 can't remember and my docs are on the machine,

Can I fit any board into the case? My preference would be to not go back on processor so that bundle looks good if it will fit.