//...as the rent was paid up to the end of the month, I had until then to clear the flat.//
But were they not simply giving you that time to remove anything you wanted to keep, Sharon, after which they would dispose of it?
Generally speaking other people are not responsible for clearing properties in these circumstances. Apart from anything else, who would the responsibility fall to, bearing in mind that "next-of-kin" has no legal standing whatsoever? The property owner might make a claim on the deceased's estate (though I'm not sure whether that would succeed). But if there is no estate to speak of....?