Hey Richard,
Algae is caused by a combination of two problems, and is symptomatic of the problem, not actually the problem itself (in the same way that your "CHECK ENGINE" light means something is wrong with the car. The problem isn't that the light is on, the problem is that your gas cap needs tightened. THat'll be $249.99).
The first is that there is too much light on the tank, which is pretty easily remedied, and I don't suspect the case. Either way, cutting back on the light will help with the algae, but doesn't address the bigger problem.
Algae need nutrients to grow, and those nutrients have to come from somewhere. There are four possibilities. First, check your tap water and ensure that there aren't a lot of nitrates and phosphates in your tap. More likely is that you're often overfeeding the tank. Third, you may have a stockpile of nutrients somewhere which a cleaning isn't removing -- are you remembering to lift your decorations and vacuum under them? Did you get that big dead fish that crawled wayyyy up inside of the hollow castle? Etc. Lastly, you may have a case of too much fish and too little tank -- without knowing the size of your main tank (which I hope isn't also a 20-gallon!), that's hard to say. But 35 cichlids could be too many.
Finally, when you use a UV filter, you are killing a lot of the bacteria and algae that live in the water column. The ones that live on the tank walls, decorations, etc., are unaffected -- and have less competition for the nutrients.