I feel Japan has a really low cost of living, despite what you might read. I personally spend much less here than I would in the UK.
StayDead, do you like Japanese food? Do you want to go to traditional Japanese-style izakayas? If so, the average meal where I live costs about ¥800. Maybe a few hundred more on for Tokyo (they also have cover charges in the biggest cities, where you pay about ¥300 for a table).
If you like alcohol, do a nomihodai. You might know the word already but it's ¥900-1400 or so for two hours all you can drink.
I don't live in Tokyo, but £7000 a month was presumably going on an expensive coke habit and vast amounts of prostitutes. I'm not prudent at all with my cash here (and admittedly I am not a tourist) but if your rail travel is all included, you shouldn't be racking up such a bill.
I had friends visit for 2 and a half weeks and, while they did stay with me for four nights, they only spent about £1600. That is including accommodation and the rail pass. They spent about £900 in terms of spending money.
And we managed to do Tokyo , Osaka, Nagoya, Kyoto, Nikko, Koyasan, Nara, Takayama and Hiroshima.
Admittedly the pound was stronger then, but if you avoid tourist traps, stay in Air BnBs and Guest Houses (or hostels), avoid western-style food or restaurants and resist the urge to buy loads of tat simply because it's covered in kanji and looks exotic, then you easily do a trip for a similar price. And we covered the breadth of Honshu.
Though if you want to splurge, and shop a lot, then you should save up, as it's pointless coming here and penny pinching. My friends and I weren't on a budget at all, but I imagine it's not somewhere you want to have to wait your whole life to visit and then scrimp and save each day.
We didn't live frugally at all however, and they still didn't spend that much. It's not half as expensive as people make out. Especially if you're not just confining yourself to Tokyo.
As you've wanted to come here for ages, I would honestly make time and money no object. Or consider bagpacking with the rail pass. The Shinkansen and rail pass make transportation to the major areas an absolute steal. As a resident it costs me about £150 if I just want to do a return trip to Tokyo from Nagoya.
You can also fly too, with some low cost carriers such as Peaches, JetStar, Air Asia etc.
My other big tip would be to abandon preconceptions before you come, and not treat your first experience of Japan as a "test". It's just another country, not heaven.
Yeah, Akihabara is great but about as far removed from every day life as people in Britain wearing bowler hats 24/7. It's purely anecdotal of course, but the people I know who came here with expectations as to what it is like, all went home fairly quickly. Conversely, I came here with a relatively open mind, and without being bothered about the whole anime, manga, j-pop, games sub-culture (all not as prevalent as you might think in my opinion) and I was able to adapt fairly well and am still here.
Don't treat it as a test. Your trip isn't something Japan must pass. Don't stick that burden on what is your first taste of things. And don't expect to be miraculously changed when you come here. Too many people think that Japan is the answer to all their problems and unrealized dreams. It's not. It's another first world developed nation with all the problems and modern frustrations.
One last things too. Your Japanese language skills probably aren't going to be as good as you think. Maybe it was just me, but I vastly overestimated how good at speaking I was going to be. You might find it a bit of a shock, especially being self taught.