Hi Mariner,
There isn't that much in Birkenhead itself these days, but there are several clubs around Wirral and in Liverpool: look in the Folk Orbit website under Local venues. The listings are by the historic counties, by the way.
There are some occasional folk concerts at the Pacific Road Arts Centre in Birkenhead (including an appearance by Martin Simpson on 8 Oct 2004), and, if you are still around then, the Liverpool Irish Festival takes place from 21st to 31st October 2004.