M-W is relatively new to the usage business and it wouldn't altogether surprise me if they were just wrong. OTOH they tend to be strongly descriptive, so it's also conceivable that they're merely reflecting a relatively recent change in British usage that traditionalists might have described as a decline in standards.
Garner, Dict. of Modern American Usage:
"INQUIRY. ... In AmE, 'inquiry' is the standard spelling in all senses. In BrE, 'enquiry' is equivalent to 'question,' whereas 'inquiry' means 'an official investigation.' See -EN.
"EN-; IN-. No consistent rule exists for determining which form of the prefix to use before a given word. But it's fair to say that the French form 'en-' is more a living prefix than 'in-.' ...
"Preferred Form: embalm, embark, embed, embitter, emblaze, embody, embolden, embosom, embower, embrown, empanel, empower, encage, encapsulate, encase, enclasp, enclose, enclosure, encrust, encumber, endow, endowment, endue, enfold, engraft, engulf, enlace, enmesh, ensheathe, enshrine, ensnare, ensoul, ensphere, enthrall, enthrone, entitle, entomb, entreat, entrench, entrust, entwine, entwist, enwrap, enwreathe; imbrue, impale, impoverish, inflame, ingrain, inquire, inquiry, inure.
"Especially troubling to writers are word pairs with varying prefixes according to inflection: 'enjoin' but 'injunction."'