To sustain a claim to legal advice privilege, the relevant document or communication must be created or sent for the dominant purpose of obtaining or receiving legal advice – see Civil Aviation Authority v R Jet2.com Ltd  EWCA Civ 35.
If the sole purpose of the document or communication is to obtain or receive legal advice, then the ‘dominant purpose’ test will be satisfied.
If, however, a document or communication has been created or sent for a dual or multiple purpose(s) (for example, an internal investigation report for remedial purposes as well as to ascertain rights and liabilities in actual or contemplated litigation) it will be necessary to show that ‘giving or obtaining’ legal advice was the purpose for its creation. A secondary, or even equal, purpose will not be sufficient. Whether the ‘dominant purpose’ test is met is an issue of fact that the courts will consider from an objective standpoint.
Difficulties may arise when ascertaining the dominant purpose of multi-addressee emails sent simultaneously to various individuals for their advice or comments, including a lawyer for their input.
If the dominant purpose is to obtain the non-legal or commercial views of the non-lawyer addressees, then it will not be privileged, even if a subsidiary purpose is simultaneously to obtain legal advice from the lawyer addressee(s).
You may wish to analyse the email by considering them as separate communications to each recipient and asking whether if the email were sent to the lawyer alone, it would have been privileged. If the answer is no, then it is unlikely that the same email to the other recipients will be privileged. If the answer is yes, then the question arises as to whether the email to the non-lawyers is privileged, because in substance its dominant purpose is to settle instructions to the lawyer (as between the non-lawyers) or to disseminate legal advice.
It is also worth bearing in mind that if the legal and non-legal advice in the document is sufficiently separate, it is usually possible to redact the genuinely legally privileged parts of the document (see GE Capital Group Ltd v Bankers Trust Co  1 WLR 172).
Additionally, if the legal and non-legal parts of the document are so intermingled that distinguishing the two and severance are impossible for practical purposes, then the courts have indicated that they may accept that the dominant purpose of the whole document is the giving or obtaining of legal advice (see Civil Aviation Authority v R Jet2.com Ltd  EWCA Civ 35).