The Oxford Advanced Learner's Dictionary has an "Help box" regarding Enquire vs Inquire, I'll paste it here:
In British English people sometimes distinguish between enquire and inquire, using enquire for the general meaning of ‘ask for information’ and inquire for the more particular meaning of ‘officially investigate’.
- "I called to enquire about train times."
- "A committee will inquire into the allegations."
However, you can use either spelling in either meaning. In American English inquire is usually used in both meanings.
The NOAD distinguishes them as inquire and inquiry being the usual U.S. spellings, while enquire and enquiry are classified as "the standard forms in Britain".