Shrewsbury Local DVLA Office Noticed some out of date information (show/hide)? Spotted a mistake? Let us know. Type letters: Shrewsbury DVLA Office has now closed. Please contact the the main DVLA Headquarters. Please Note All local DVLA offices have now closed down. You can now access DVLA services by contacting the main DVLA office directly, or using their online services. Some services can also be accessed through selected post offices.