There are a number of health cash back schemes which now cover alternative therapies such as acupuncture these schemes cover a wide range of treatments without the need for referrals which is usually the case for private medical insurance.
Some employers provide health cash back schemes as an employee benefit.
Therefore for a monthly charge with an organisation such as Healthsure you could not only recover some or all of the acupuncture costs you can also benefit from other areas as well.