Kingdoms
The UK accepted system has five kingdoms, for some it's hard to describe a single word common name so I hope you don't mind that I have written brief summaries too:
1. Animalia are multi-cellular organisms that have adaptations to allow them to move within their environment. They have membrane bound organelle but not cell walls or chloroplasts. They must absorb nutrients by ingestion. Common name is animals ;-)
2. Plantae are multi-cellular organisms that use photosynthesis to harness energy from sunlight. Their cells contain cell walls & chloroplasts (where cells are exposed to the sun). Common name is plants
3. Fungi are multi-cellular organisms with no adaptations to move independently. They range in size from microscopic to the size of mushrooms (literally, of course). They absorb their nutrients from their surroundings. Common name could be mushrooms & molds
4. Protista are marine organisms that are eukaryotoic (have membrane bound organelles) and some can photosynthesise. 1022
Common name could be algae
5. Prokaryota (a.k.a. Moneara) are single celled, with a cell wall but with no membrane bound organelles (i.e. they have no smaller 'bits' within the cell separated by a membrane). They absorb nutrients directly across their membranes or can photosynthesise to make their own nutrients. Common name could be said to be Bacteria.
Sources: 1, 2, 3 (for Protista)
Phyla and Below
You may wish to try the following website: ITIS Database - enter a scientific or common name of an organism to get it's full taxonomic tree. For example the tree for the Panthera leo (Lion). This site also gives common names of Phylum, Class, Order & Genus - for example the lion is a member of genus Panthera ("roaring cats"). It may be slightly cumbersome but it is a way to get the info you want and is actually quite interesting once you get going, particularly if its just for your curiosity!
Additions after comments by OP
Have been hard at work, however it seems that a centralised repository is certainly elusive! I've found some sites which go a little of the way to amalgamating scientific and common names on a single page but I'm doubtful that you will be able to get much further than Phylum without having to write a script to harvest data from sites such as ITIS
1. List of all Phyla for the Animalia Kingdom with common names.
2. As above for Kingdom Plantae
3. As above for Kingdom Fungi
4. As above for Kingdom Protista 389