Forgot to mention but, if you look on ebay at the moment, there's quite a few old lantern slide photographs for sale, many of which are of old Wirral and North Wales. One of these in particular claims to be of an old bridge crossing in Wirral, circ.1890-1900.
Well worth a look even if you're not interested in buying. Just type in 'lantern slides' on ebay search. There's quite a few different sellers but most of the Wirral ones I saw were on pages 10 and 11.
Sorry about that, but can't suggest much else other than checking the Greg Dawson books. He's the local expert on all things relating to Thingwall & Landican. If there was a 'Landican Bridge' anywhere in the area I'm sure he'd have written about it.
Sounds to me like it's an ancient stone bridge that you're after, in which case, it may have been part of a pack-horse route. There used to be a few on the Wirral, including the one at Storeton known as Roman Road.
Have it the river in question is marked on the map you kindly shared, not as the Fender, but the Ford Brook, and it is this which crosses the course of Landican Lane. Was the name of that river/stream changed sometime later? Does anyone have any recollection/info/maps on the Ford Brook?
The Main Fender on the map seems to me to be the Birket nowadays
The Main Fender is indeed now known as the Birket and the Ford Brook is now the River Fender, it would be interesting to find out when these name changes took place, and who's responsibility is it to change the name of a river.
God help us, Come yourself, Don't send Jesus, This is no place for children.