Using the possessive is fine here. But note, "English" as a noun only means a language. If you're talking about a country, it's "England's accommodation spending", or more likely "The United Kingdom's," since England is a subsection of the UK.

In general, it's fine to use a possessive, like "X's Y" as a replacement for "the Y of X." This could work with, say, "Americans' spending on accommodations." Note, that's both a plural ("Americans") and a possessive.

The difficulty in this case is that the plural for residents of Britain is tricky. There are many nationality-type words that don't have a convenient plural; we don't say "Frenches." You can speak collectively of "the French," but this doesn't lend itself well to a possessive ("the French's"). You might hear terms like "Frenchmen," but these are outdated and have sexist as well as perhaps racist overtones.

Things get even more complicated for England, because "England," "Britain," and "the United Kingdom" can be distinct ideas, and sometimes we carelessly substitute one term for another. If you're reporting data, it's best to be very clear. Are Scotland, Northern Ireland, etc. included? Are you speaking of an ethnic group or citizens of a political country?

So the best option is, as you suggested in a comment, to expand the phrase. Perhaps "The spending of residents of the UK on holiday accommodations." (Come to think of it, that's one that could use a plural possessive: "UK residents' spending...")

One other note: British English does speak of going "on holiday," so it's the logical choice of phrase in this case, but American English tends to say "on vacation." Or if your audience is American you might use the American phrase even when speaking of the UK.