Hi Peter,
there's loads of locals who fish off the rocks. if you walk east (walk to the sea, put the town behind you and turn right) along the coast out of Funchal, you'll find a swimming pool carved into the rock, you can walk out on some big rocks and fish. The island is so steep, you should be casting into deep water.
Its a few years since I've been, but I think you can see the spot on this google map.
Madeira, Portugal - Google Maps. Looking at the satellite map there's loads of interesting spots and there's a good path along the coast.
I've always thought there must be some local lads who would take me out with them for a reasonable amount. The guy I talked to said I could go out with him if I ever went back, but sadly I never made it back and the hotel closed. I reckon £50 would have made his day and I always thought a handful of smaller fish would be more interesting than a big game fish.
Have fun, let us know how you get on.
Cheers
Andy