Although a lot of plastic bottles in the UK are recyclable, not many of them actually make it to the recycling bin. Also most plastic bottles in the UK are manufactured in China, so they have already travelled nearly a third of the way around the world before they get to the UK. Each plastic bottle will be placed within an individual plastic bag, to protect it on its journey so that's a lot of plastic.
By switching to a plastic-free shampoo you are eliminating the need for plastic, plus the ingredients are organic, cruelty free and handmade in the UK.