What is the maximum current a 13Amp twin wall socket can handle?
Assuming your country is the UK, this is a bit variable, they are all good for a total of more then 13A, but how much more....  

Most common 13A double sockets are good to about 20A total across the pair, the exception being the MK stuff which is capable of the full 26A. 

Check the datasheet for your chosen part to confirm, but IIRC only the MK ones (and possibly only the MK Metalcad ones at that) are specified to the full 26A.