This is a surprise to me. I haven’t heard of interest being left in an ISA once it is closed.
I’m going to ask around some financial companies to see if any of them have a view on this, but my feeling is that if there is money left in your old ISA, either take it out if you would like to spend the money or have it transferred to your new ISA (speak to your current provider to contact the old ISA provider and move the money ‘behind the ISA lines’!)