Today I have visited the new AMICS office in Torrevieja (The new agency set up by the Valencian Government to help foreigners with all issues relating to living in Spain) which is situated next to the Town Hall in the church plaza (it used to be the International Residents Office) and the helpful gentleman told me that now people living and padroned in Torrevieja can apply for their residents certificate (either as 1st timers or to replace expiring residents cards) in Torrevieja in the office located in Calle Maldonado (top end off Gypsy lane neat the windmill) and do not have to go to Alicante.  I gather it is also possible to make an appointment to save hours of queuing!

This office also issues NIEs (but not the same day)