I Would Certainly Hope There'd Be Reciprocity
My wife and I travelled through the Cotswolds last Spring while making ample use of our own disabled parking permit. We don't call them "Blue Badges", but they are blue plasticized cards with a wheelchair icon, about 8" by 3", meant to hang from the windshield's rear-view mirror. Since ours was recognized in the UK, I strongly suspect that yours will be recognized in the US. You might want to check with the RAC or AA (Are they both still in business?) just to make sure, but I would not anticipate any problems.
AZBuck
If you don't have time to get the CA permit...
Why don't you get a lanyard that has the gripper teeth and just use that to hang the UK disabled pass from the rearview mirror? Or some similar set-up. I would imagine it would be honored as long as it's hung from where people in the US normally look. But I think I would contact the CA DMV and ask. I'm sure they must have email addresses posted on their website.
California DMV Vehicle Code 22511.5 Foreign Disabled
Hi
I used to have my application for a Visitors Travel placard by sending my application to the DMV in Sacremento and then it was processed, paid and collected at the local DMV office in Concord.
My application was completed and signed by local GP as like most visitors to California I do not have a physician in the US.
In 2005 I was told that I no longer need to obtain a California DMV placard as I could use my own badge issued from the UK and if needed I could quote the California Vehicle Code 22511.5 (b), which allows for Foreign Jurisdication issued placards to be given the same parking privileges authorised in Vehicle Code 22511.5.
It is worth taking a printed copy of the Vehicle code that can be displayed on the dashboard alongside your own badge. Though, I have never needed it as enforcement officers accepted I could use my badge.
http://dmv.ca.gov/pubs/vctop/d11/vc22511_5.htm
(b) A disabled person or disabled veteran is allowed to park a vehicle displaying a special disabled person license plate or placard issued by a foreign jurisdiction with the same parking privileges authorized in this code for any vehicle displaying a special license plate or a distinguishing placard issued by the Department of Motor Vehicles.
Hope this helps.