Hi Andy, dont know if this will be of any help, as the last time I was in Madeira was 2005, but anyway.... I took a 3 piece beach rod with me,and a Shimano exage spinning rod, and fished from the old pier shown on the attached picture.
You should be able to pinpoint it from Google earth,thats where the picture is from,you can see the main harbour to the right.The local anglers were fishing from it, those fishing for the pot for small stuff from the landward end, those after larger fish, using Beach rods and reels from the seaward end.
The barman at our hotel ,who was an angler took me there, casting out into deeper water I caught Trigger fish,and some decent "Bream" ( I think ) and was smashed up by something large that didnt want to play. There were Mullet swimming around the pier, plus some larger fish that were hunting small stuff, I should have had a chuck with some lures as I am sure they would have worked, but I was too interested in the Triggers etc.
I was told that there were Conger close in,amongst the rocks,and Ray at distance, but never saw them myself.
For bait, I used prawns and some mackerel like fish from the supermarket.
If you look on Google earth, you can see a black line down the centre of the pier, it is a channel, about a foot deep and the same wide, at the end of the channel at the seaward end there was a hole about 2 ft square that was about 20 feet deep, with water at the bottom, so be careful.
I cant remember the name of the hotel we were in, but it was only a 10 minute walk away, and the supermarket was on the right hand side on road down to the pier, next to a cafe.
I would recommend the basket sled trip on the road down from the Church on the hill above Funchal town, very ..... different !
See below.. in German, but gives you a taste.