Suggest you visit your local marine shop Warren. There are a number of products around for cleaning oxidised aluminum. BLA Aluminium Cleaner is one I have used on my boat that works well. A weak acid is safe but most purpose aluminium cleaners (including wheel cleaners) will have something that decomposes into hydrofluoric acid - not nice stuff in concentrated form (which it won't particularly be in retail products) but very effective. Suggest you stay away from anything caustic based (like oven cleaner) . Caustic (sodium hydroxide)  dissolves aluminium turning it back into good old bauxite, from whence it came ! Use enough and you will end up with a pitted surface. Good old fashioned metal polish and  a buff work best if you want it really shiny and can get the access. Biggest problem is that after all your hard work, raw aluminium is a reactive metal so will tarnish again quite quickly.