Okay, your Asus Essentio CM6730-UK20S computer doesn't come with a lot of information and a lot of it is bundled under the CM6730 books as "here are the possibilities the system can be"
I need you to look on the Motherboard itself for an Asus Motherboard Number if possible. usually located near CPU or PCIE Slots. Look at the image below for an example of what you are looking for (the white label , in this example this is from a CM6650 Board) but the numbers before it is what I am looking for.
Now an educated guess without that very specific information, and based on Asus Web site (https://www.asus.com/ae-en/Tower-PCs/Essentio_CM6730/specifications/) the Asus CM6730-UK20S system, it looks like you can upgrade from 4GB to 8GB of ram Dual Channel, DDR3 at 1333MHz and you can only use 2 Ram sticks, which would look like 2x4GB DDR3-1333MHZ as max memory upgrade for this board. One must still get the motherboard information (or information from your current ram stick) to make sure it is DDR3 or DDR3L type ram as one is 1.5v the other is 1.25v and are not interchangeable.
Asus says DDR3-1333 and www.Crucial.com states DDR3L type ram (http://www.crucial.com/usa/en/compatible-upgrade-for/ASUS/cm6330cm6630cm6730cm6830) so I will wait on your information on your current ram to make a suggestion. But if we can find a matching ram to your current 4GB (if single stick) we could keep cost about 50-60 Quid.
As for a video card your Asus CM6730-UK20S System has a single PCI-e x 16 Slot for that purpose. that said, since they do not specify what version that slot is, I will base myself on the "optional hardware for video card they suggested to buy for this system (see ASUS link above) and look at the AMD Radeon HD7470 1GB which is a PCI Express 2.1 x16 video card. (ref: https://www.cnet.com/products/amd-radeon-hd-7470-graphics-card-radeon-hd-7470-1-gb-series/specs/) so I will assume you Slot is also 2.1x16 which is pretty good news as it opens a lot more cards than not..
Now that said the specs on the Asus Cm6730-UK20S is indicated to have a stock Power Supply of 350W Peak.
This factor alone will define how big a video card you can have (example a HD 7870 needs 400w and a PCIe 6+2 connector which your PSU does not have) But again this only will guide your path to upgrading this system later, as your case is a standard ATX so you will be able to get aftermarket PSU installed and get bigger video abilities.
Now all that said, and considering you Budget of 100 Quid.
video card wise your looking at maybe a GT730 2GB for about 50 Quid, or a GT 730 4GB for 85 Quid, there is a better card still GT 1030 2Gb for about 65 Quid.
Here is a comparison of the OEM 7470 GT 730 2GB and 1030 2GB cards side by side, just to help you choose.
I am sure other will suggest other cards, I don't know everything of course.
until you upgrade the PSU you will be limited to low powered video card.
The suggestion above of the GTX750TI is a really good one, but your looking at used cards on ebay or such places. and take risk cards where not abused and or cooked in ovens to make then work again.