Not quite true on the VAT. "There is VAT on second-hand goods if the seller is VAT registered. Generally, businesses are required to register for VAT once their taxable turnover reaches £85,000 for 2019/2020. "
The carnet article is interesting too: "Minister Dinenage confirmed that a simple ‘oral declaration’ could be made by musicians who are travelling with portable musical instruments and that a costly ATA Carnet would not be required. Musicians transporting instruments and equipment by car, van or truck would require a Carnet, however,..."
But you're one bloke with a bass so you're fine. See you in September!