I often change my plates and take the paperwork to a local DVLA office.
in Wimbledon.
However if you are unable to send them off do not send them to the Swansea office but this one.
http://www.dft.gov.uk/dvla/contactus/lo ... ffice.aspx
I know someone who works there and they told me that unlike Swansea they have not got a great deal to do.
I had a log book turn round in 4 days there and put a retention on a plate in 6 days.
Hope this helps.