I didn't understand the "cutting ties with the tabloids" announcement. As much as I detest the UK tabloids, they can write articles about whoever they want. They don't need someone's approval to write an article about them. "Cutting ties" is not going to make the tabloids stop H&M stories. There's also nothing to stop the tabloids writing stories about H&M based on stories from other media outlets, e.g. "In a shockingly horrific revelation, the Duchess told Vanity Fair magazine that she married the Duke for his money". (ETA: Like the Sun story linked above, where the Sun is writing about the H&M birthday call to the Queen, and basing it on a Daily Mail story.)
The tabloids can also still phone H&M or their representatives for a comment or a response. But just like anyone else, H&M or their people can say "no comment" and hang up.
One thing I was wondering about this, too, is that some of the tabloid coverage, especially the photos, comes from agencies/cooperatives that the media outlets pay to belong to. Using content from these sources is becoming more common as newspapers cut back on having their own staff and photographers. H&M have no way to stop the tabloids using material from those sources, nor should they, because the tabloids have purchased the rights to use that material.