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Could do it all with push fittings and plastic 15mm. The top pipe in the picture looks like it has a non return valve on it (to the left of the t joint).
Having had something of a look around 15mm copper and stainless pipe is common here, but plastic pipe is only in 1/4" and is universally referred to as water filter pipe. There are quick connect (as push-fit is known) for that diameter, but at 15mm it's all brass compression fittings.
I might buy a few bags of 15mm push fit and some 15mm plastic pipe when I am in the UK over Christmas and take it back with me, as it'll look a bit less out of place above the counter top and be easier to route due to the bendiness factor.
Could do it all with push fittings and plastic 15mm. The top pipe in the picture looks like it has a non return valve on it (to the left of the t joint).