via Athens by road
The drive down from Venizelos airport in Athens to the southern Peloponnese has been improved dramatically by the construction of the Athens ring-road and improvements to various segments of the motorway south of Corinth. If you are heading to Kalamata, this drive now takes less than three hours. It is another hour south to Kardamyli/Stoupa. Tolls will cost around 15 euros one way. At Tripolis, there is the option to turn off to head to Gythio to enter the Mani this way. This segment has as yet (November 2012) not been completed.
via Kalamata by air
The good news is that for the summer of 2013, Easyjet will (at last) be running scheduled flights from Gatwick to Kalamata. More details here. Alternatively, Thomas Cook offer chartered flights from Gatwick and Manchester. A taxi from Kalamata airport to Kardamyli/Stoupa is about 60 euros and takes just over an hour. The taxi rank always has drivers waiting for fares.