For some reason, there is little biographical information regarding Heathcote on the Web. Sources with sketchy information are here and here. One site I stumbled across hinted in passing that he attended Harrow, and a partly blocked Times of London piece dealt with Heathcote's renovation of his house in the tony Chelsea (in London) neighborhood. So I must assume that he is doing fine financially, unlike many artists.
Heathcote has a Web site that's worth viewing. This page and subsequent pages feature his paintings, the titles of which are cryptic and that I ignore in the presentation below.
Are his paintings Dieselpunk? Maybe, according to this post on a Dieselpunk site. I'm inclined to think not. That's because most Dieselpunk art alters actual 1920s and 30s objects as if they were in a parallel universe. Heathcote instead takes objects as they were and does his time-warping by the inclusion of non-period (in terms of dress) people.
Like Retro artist Robert LaDuke (see my post here), Heathcote recycles themes, settings and objects. See the images below for examples.
Jack Vettriano, but lack the tension and sense of potential menace often present in his work.
I've never seen a Heathcote painting in person, though I'll be on the lookout when I'm near a gallery that carries his work. This means I must evaluate on the basis of images such as those displayed above.
Despite what I noted in the various comments above, I rather like his painting. Yes, it's more hard-edge than I usually prefer, but the point is to portray 1930s stuff clearly, unambiguously. The people in his paintings are pretty repetitious in terms of pose and costume details, but that's something one notices on a Google Images spread or assembled on a blog page. In isolation, a Heathcote might be quite interesting, especially if juxtaposed to different kinds of paintings or else perhaps placed near a group of Art Deco objects.
I'm not prepared to claim Heathcote's work great any more than I am Vettriano's, though I find both strangely appealing due to their subject matter. In Heathcote's case, I pretty sure it's because I'm a sucker for the elegant aspect of the 1930s, wisps of which persisted into my childhood years.