Far better to book a mobile skip (ie a lorry with 2 blokes who will fill the skip for you and then take it away) rather than a static skip which requires paying for a permit and doing the humping yourself. I have used Pontypool Skip Hire (now Full Circle Recycling of Cwmbran/Pontypool) twice. You pay for each cubic yard/metre they take. I think their biggest lorry is about 24 cu yd. They are also on Facebook.

https://fullcirclerecycling.co.uk/contact/index.html

StT.
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