From your description, it does sound like you have an issue with fleas.
You have used quite a few products in a short space of time, and unfortunately quite a few of these off-the-shelf products are not that effective.
My advise would be to wait until at least 48 hours from the last time Alfie was bathed, then apply a more effective spot-on treatment to him. If Alfie has been seen by his vet in the last year, you should be able to purchase something from them. If they are not open today, the best off-the-shelf product you can use is Advantage. I would not reccommend using any of the others.
You need to wait to bathe Alfie for at least 48 hours either side of application as the spot-ons dissolve into the natural oils of the skin. So you need to allow the skin to replenish its oils before applying it.
Once you have treated Alfie, Advantage will spread over his body in the following 12-24 hours, killing in-catact fleas in 1-2 hours.
If you are concerned about the fleas spreading through the house, then I would advise washing Alfies bedding at at least 60'C, and possibly also treating the house with a spray as well. I usually advise a product called Indorex, but there are actually many good hosehold products.
Once you have treated the house, it is best to vacuum thoroughly. If you use a vacuum cleaner with a bag, I would change the bag after this vacuuming as the fleas can live in your hoover bag!
I hope this helps and if you have any follow up questions, please don't hesitate to reply to me