Hi Reddish,
Welcome to the forum.
If I've understood correctly, you have a key that is just the top half and doesn't have the three buttons for the central locking?
If so, then you'll be needing a replacement remote half of the key, of which there are two options for the A2 dependant on the CCCU fitted. To check which CCCU is fitted, lift the passenger footwell carpet and the Aluminium plate beneath it and look at the top black box. The part number will be stamped on the top.
If your CCCU is 8Z0 959 433 Q, then you require the remote half of the key with the part number 8Z0 837 231. Note there is no letter after.
If your CCCU is 8Z0 959 433 AF, then you require the remote half of the key with the part number 8Z0 837 231 D. Note the 'D' is important.
The remote half can then be programmed to the car using VCDS, which many people on here own or have access to. It is not essential to have two keys paired to the CCCU as Stockport Audi suggest, as far as I am aware.
Regards,
Matt.