Totally okay to live off in London. I feel like often people can be very dramatic about living in London but there are ways to reduce your living expenses, it's just that many are not prepared to make them. Most people our age don't live on their own in London - housesharing is often the default for people in their 20s even at higher salaries, and that substantially reduces rent. Try and get a deal where you pay the landlord bills and rent in a fixed sum and then it's easier to budget. I've found some for £500-600 bills included which gives you enough left over for travel (which would be higher as cheaper rents are less central but again you can cycle/walk where you can), food, luxuries etc. Just fyi as someone above mentioned this, but you won't be paying student loan at that salary and normally you can opt-out of pension schemes when young. And to be honest when you're young you kind of get used to having a lower than ideal living standard - we've just been students after all!. It's when you're older and you can't afford the things you want that it will start to grate. If you don't get a pay rise in 6 months you can move on to another job.
Any salary is better than no salary. But if you have other AC's along the way I would accept the job (it will take a while for the contract to come through), but go to the ACs and see if you have any luck with them. Then it's a win-win. But would remind you that you are young and have nothing to lose from this job. Even if you do it for 6 months that's some experience, if you get an AC you may spend 6 months doing nothing anyway if you start in September. You can easily move around jobs, especially in London and when you don't have any children or a mortgage to think about.