There are international flights to Tokyo’s Narita airport, Osaka’s Kansai airport, and Nagoya’s Chubu airport – all of which are on the main island of Honshu – and plenty of domestic airports serving internal flights. London–Tokyo prices start at c. £400pp return, with the flight taking about 11hrs 30mins.
Japan is 11 hourrs ahead of GMT, which means you should expect to suffer significant jet-lag on the outward journey. UK citizens don’t need a visa for Japan.
Travel within Japan can be excitingly futuristic, from the famous 300km/h bullet trains (shinkansen) to Tokyo’s Tama monorail. Japan’s train services are not only fast but incredibly efficient and punctual. If you plan to use the train a lot, it’s worth investing in a Japan Rail Pass, which includes travel on the vast majority of trains, from little mountain railways to long-distance sleepers to the north, and will save you lots of money and queuing time. (You need to buy it before you come).
Car-hire is only really necessary if you’re going to be exploring rural areas or the sparsely populated island of Hokkaido.