03 numbers are UK-wide numbers. They are not associated with any particular location, but are charged at the same rate as 01 or 02 numbers.
Within the 03 ranges there is a group called "Mirror Numbers" which are specifically for those with 0844 numbers.
Mirror Numbers effectively are the 0344 version of your 0844 number. If you already have 0844 123 456 then you can have the "mirror" 0344 123 456.
Calls to 0344 numbers cost no more than calls to geographic numbers (01 or 02) and are included in inclusive minutes and discount schemes in the same way, which could mean more calls for you.
Calls from landlines are typically charged up to 9p per minute
Calls from mobiles typically cost between 8p and 40p per minute
Calls from landlines and mobiles are included in free call packages.
Using the 0344 mirror to your 0844 number gives you more flexibility in handling incoming calls and provides a cheaper method for your customers to reach you.