I'm not suggesting in any way that Hammer's early horror pix were literally intended as follow-ups to the earlier American film but rather that its success may have been a factor in Hammer's getting into horror the way they did, in period and in color.
Perhaps the success of HOUSE OF WAX was a factor in prompting Milton Subotsky to write his FRANKENSTEIN script; perhaps not. (Does it get a mention in the story of Amicus in the recent Little Shoppe of Horrors magazine issue? I'll have to look around for mine).

However, the problem with assuming that Hammer singled out HOUSE OF WAX and figured it did its great box office because it was a period horror film in color ignores the more likely scenario: by that time, most probably concluded that HOUSE OF WAX did so well because it was a 3-D picture made smack in the middle of the 3-D craze. Like I said, THE MAD MAGICIAN (also in 3-D) is the best example of an immediate attempt to cash in. Warner Bros. itself does try another period color horror the next year with PHANTOM OF THE RUE MORGUE (1954), but neither it nor MAD MAGICIAN seem to come anywhere near matching HOUSE OF WAX's success.

As Ted points out, Hammer had plenty of more direct influences right in its own recent production history: Richard Wordsworth's Carroon in QUATERMASS EXPERIMENT is very Karloffian (complete with encounter with innocent young girl who's playing), while Brian Donlevy's hard-charging, single-minded Quatermass certainly shares some traits with their later take on the Baron. And, of course, one of their chief American investors comes to them with that Subotsky-penned Frankenstein script (which eventually gets discarded).

As for why Hammer did their horrors in period (while Universal's DRACULA is contemporary as is, less obviously so, FRANKENSTEIN), it should be remembered that they went back to the original source material, the novels, rather than merely copying the Universal films approach.