I was made redundant back in February. Since then I've probably made 120+ job applications. I'm just waiting for a date and time for my fourth interview. A fair chunk of the applications were for jobs that would have been a bit of a stretch but the vast majority were for jobs I could do in my sleep (IBM Mainframe operations analysis, CICS/Cobol development and a bunch of other stuff). There will always be companies that have a very rigid recruitment process (usually with a defined list of skills requirements) but there are also places around that can see beyond your basic skill set. One of the interviews was for a position that did not involve a single technical skill on my CV. They just liked the fact that I hadn't been changing jobs every couple of years but also had a wide variety of skills and experience.
The bottom line is that unless your time is very limited then it's worth applying. I know it's possible to register your details directly with companies, The last time I was made redundant (back in the eighties) I was contacted a couple of months after a "failed" interview for another position. The company had retained the CV I sent in for the first position along with notes made by the initial interview.
Anyway, keep your fingers crossed for me. I'll let you know what happens.