As suggested in the following extract from Oxford Online Dictionary, there is not much difference in usage between enquire and inquire, apart from the fact that enquire is more common in BrE while inquire is more common in AmE:
The traditional distinction between the verbs enquire and inquire is that enquire is to be used for general senses of ‘ask’, while inquire is reserved for uses meaning ‘make a formal investigation’.
In practice, however, enquire, and the associated noun enquiry, are more common in British English while inquire (and the noun inquiry) are more common in American English, but otherwise there is little discernible distinction in the way the words are used. Some style guides require that only inquire or only enquire be used.
- Could I enquire about your mother's health?
She inquired about the library's rare books collection.
Every enquiry is very welcome.
Adam helped the police with their inquiries.
The Grammarist notes that:
There is one qualification to this. Some Britons make the distinction that enquire and its derivatives apply to informal queries, and inquire and its derivative to formal investigations. While this distinction appears widely borne out in more carefully written British texts, it is less pronounced in more informal types of writing (some news websites, some blogs, web comments).
Also the following source confirms that both form would suit informal and formal contexts, but inquire appears to be the preferred spelling:
In practice, enquire and enquiry are more common in British English, and inquire and inquiry are more common in US English, for both informal questions and formal investigations. However, the Guardian (a British newspaper) tells writers to “use inquiry” and the Oxford English Dictionary seems to recognise inquire as the more dominant form, deeming enquiry:
- ”An alternative form of INQUIRE. The mod. Dicts. give inquire as the standard form, but enquire is still very frequently used, esp. in the sense ‘to ask a question’.”
So, it’s up to you which spelling you use, though if you’re writing for a particular publication, it’s worth asking about their house style. Sticking with inquire is probably best if you’re at all unsure, and whichever you pick, be consistent!
