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then they will be making a small claim and charging storage
That seems unlikely. I know of situations of sellers offering to guarantee things on a house they're selling and solicitors advising buyers that such guarantees are worthless, since the only way of enforcing it would be via a small claims court, which would cost thousands of pounds to go through anyway. So, if you do just ghost them it will be much more cost effective for them to just hire a man and a van to take it all to the tip than to try and compel you to do it or pursue you for costs.
Of course IANA lawyer and your conscience may require you to clear it up anyway.
Could you offer to come and collect it? I can’t actually see what they could do that wouldn’t cost them as much as they’d stand to get back off you. How much stuff was it? A car load? Van load?