I am on "annual leave"?

Solution 1:

It might be a slight misnomer to refer to it as "annual leave", but I would interpret it as follows.

Most employees have an annual-leave entitlement of x weeks; in the UK typically 4 - 6 weeks per annum. Depending on their particular employment, there could be restrictions such as not being allowed to take more than 2 weeks leave in a single block. So someone might take, say, 1 block of 2 weeks, plus 2 blocks of 1 week each, to make up their total annual entitlement of 4 weeks.

Any of these blocks might be referred to as "annual leave", it being part of their annual-leave entitlement. This would also distinguish it from:

• sick leave (when they are unwell);
• compassionate leave (e.g. because a close family member is very unwell or has died);
• any other types of special leave or discretionary leave;
• someone just being absent from the office because they are away on business; and
• time off in lieu, e.g. time off instead of overtime pay, or because of having worked on a public holiday (see definition below).
  [In this respect, my mother once received a note from an employee asking for time off in loo, loo being a British colloquialism for toilet or lavatory.]

Addendum
I omitted to explain the meaning of "annual leave". It refers to the amount of paid time your employer allows you to take as 'holiday' (UK) or 'vacation' (US) days over a period of one year. In the UK, some of it may be taken in blocks of just 1-2 days so as to have, e.g., a 'long weekend'.

Addendum 2
This usage of "leave" as a noun is defined in Chambers Dictionary as follows:

leave noun
1. permission to do something.
2. permission to be absent, especially from work or military duties.
3. permitted absence from work or military duties.
4. the length of time this lasts • took a week's leave.
5. old use a formal parting or farewell.
on leave officially absent from work.
take leave to assume permission.
take leave of one's senses to become irrational, especially suddenly and without any apparent reason.
take one's leave formal, old use to depart.
ETYMOLOGY: Anglo-Saxon leafe permission.

Definition of in lieu:

lieu noun
in lieu instead • got time off in lieu of overtime pay.
ETYMOLOGY: 13c: French, meaning 'place'.

Solution 2:

While Trevor's answer explains the vacation policy in the UK very nicely, if I, from the US, would see that e-mail auto-response, I would be confused as to what an "annual leave" is but as long as a return date was included in the auto-message, I'd assume it was a vacation or similar leave.

Though this is kind of off-topic, an auto-response from a business e-mail should probably simply state, "I will be out of the office from (date) until (date) with limited ability to check my e-mails. For immediate assistance, please contact (name) at (e-mail) or (phone number).