The OFT (Office of Fair Trading) has issued an 'invitation to comment' on the acquisition of The Book Depository by Amazon.
Written representations about any competition or public interest issues can be sent to the OFT- details here. This is open for comment until the 18th July. (They apparently expect to have made a decision on referal by the end of August.)
You can read more on the Bookseller.com website.
Obviously the 'invitation to comment' does not necessarily guarantee an investigation, but it's part of the process that leads up to it.
This acquisition could take a long time to occur...