Hi. It's a lovely room. I think given the amount of grey I'd go for a green rug, maybe patterned, which should work with your floor. It seems a little hard to find one though so I'll post any I come across!

https://www.modern-rugs.co.uk/product/designers-guild-fronda-moss-rugs

I'd tie in the seats with cushions either white and grey patterned or with the pink and green and then add solids, textures etc but they don't all need to match. The floral one on the green sofa seems to work well

https://www.oka.com/calla-cushion-cover-large.aspx?vid=QCH294GRM-0

throw https://www.oka.com/eliza-paisley-throw-muted-colours.aspx

I like the first one Gina posted. I'm falling miserably to find something with green in! Updated classic:

https://www.therugretailer.co.uk/cameo-fedra-lichen-green-8248.html

Or this may work with the grey border and pattern

https://www.frenchconnection.com/product/homeware-collection-rugs/862d8/poppy-field-rug.htm

If you have pets or children go for a synthetic polypropylene rug as it would be easier to clean. I would stay with tones of grey in this room maybe a deep shaggy one to add texture.

You can position the rug in a few ways. The French connection one is quite small but if you were adding a coffee table it could just sit under that which would work well. Alternatively FC layer their rugs (and break some rug rules!) but it may not be to everyone's taste. If you google images of "French connection rugs" there are a number of ideas

lovely room, you could get away with so many different options but I would go for something blue (trellis pattern would be nice) which would tie in with your fire place, there are loads around but the link below will show you what I mean. I tried to just link the picture but it won't work for me for some reason. https://www.wayfair.co.uk/Hand-Tufted-Navy-Area-Rug-BRKB1077-BRKB1077.html Would love to see the finished room when you are done!

lovely room. I would recommend an abstract rug with strong colours , like fushia pink and lime green

Carpet Sign have a range called Cameleon, which lets you combine any two or three colours in a lovely colour gradient: http://www.couchpotatocompany.com/products/cameleon-rug

If you are more into flat-woven rugs, you can also check out the Hanna rug by Kasthall - you can choose your own custom colours and patterns for each of the stripes:

http://www.couchpotatocompany.com/products/kasthall-hagga-hanna-rug

I know you are saying you want something with green but have you thought of a blue rug? A deep blue with not much pattern to tie everything together and bring some groundless to your space. At the moment everything is grey, pale or pastel colours with pattern or solid surfaces and the space needs an element of groundless to bring all elements together. The colour blue is the number one colour that is easiest to perceive by the human eye, therefore it will never feel heavy or overwhelming for you to look at. It will also provide a nice complimentary composition for all your other accent colours. I wouldn't use green as the wrong green can be very harsh to the eyes. Green and grey are also two colours that are currently trendy but will be out of style soon, when the trend is over.

Lovely room. I would put down a light grey reindeer rug, it would add some lovely texture and added soft luxury.

You could go for a graphic pattern with this pink rug - https://www.therugseller.co.uk/search-viewproduct.asp?id=32102&n=1

Or something more neutral with this grey one - https://www.therugseller.co.uk/logan-rugs-lg08-in-charcoal-and-ivory/p-31-19582-28623-7