Gavin,
If you haven't made a mistake in reading the serial number and it really does match what is said in the Walter book...(and he didn't make a mistake transcribing it either) then the gun is in fact the same gun. There would be only ONE 1937 S/42 Mauser Luger with the serial number 4125u.
How this would affect the value of your Luger in the UK would be entirely up to who might want to buy it and whether or not knowing some of the history of the origin of the gun was important to the buyer...
It would be interesting to see if you could find out the name of the German sailor who surrendered it, and if he was still alive, confirm that the pistol is the one he surrendered. If ship's logs are public information, it would seem to me that the information regarding the capture of the pistol, by serial number would be part of that entry in the log...
I presume that your gun has been "deactivated" according to UK law... which would drastically reduce it's value here in the U.S.
Welcome to the Lugerforum, you are surrounded by fellow sufferers of the Luger "bug" affliction.