Congrats on securing a place for the London Marathon!
I'm definitely no expert or by any means experienced, but thought I would offer my view from a newbie perspective as I have recently completed my first marathon!
I started running in the new year, so in total I've been running for 10 months, but in terms of marathon-specific training with long slow runs it was 5 months. But when I say 'marathon-specific' I must admit I did not follow any structured plan...
So did I find this was sufficient preparation for the marathon? Well, yes and no.
I think the time scale I'd allowed myself was long enough (and I think probably 6 months for you could be OK too) - but I after the marathon I definitely realised that I should have been more structured in my approach and I should have clocked up more training miles.
I felt on good form before the marathon and quite confident after completing a half marathon a few weeks prior, achieving my goal time. And physically, the marathon wasn't the absolute beast that I thought it would be (I didn't hit that dreaded wall or suffer any cramps, injuries etc) but psychologically it was so much tougher than I'd expected!! The second half of the marathon was considerably slower than my first half as I got 'the fear' and didn't know whether my legs would have it in them to go the distance. That loss of confidence was most likely due to not having clocked up many training runs much longer than a half marathon distance. And my body was probably crying out: 'what on earth are you trying to do to me?!" once I'd ventured beyond my usual training distance. I finished in 4:40 which was 10-20 minutes after my target, but felt happy to have just made it round at least.
So, in a nutshell, yes I think training for a marathon in 6 months is achievable, but with a big goal like this, I learned that I need to be more structured and disciplined to build up sufficient mileage in my training so that I am adequately prepared, not just physically but mentally as well. I learned that with 26.2 miles you can't just wing it!! Find a good training plan and stick to it as much as you can!!
If you are working towards covering a 5k distance at the moment, I would recommend, if you're not already doing this, joining your local parkrun, which is what I did to kickstart the 'structured' aspects of my running schedule. Setting aside your Sundays for a long slow run and building this up each time until you reach about 20 miles is also invaluable - this is where my own training suffered really as I wasn't disciplined enough with them. You have to be prepared to make some 'sacrifices' in your lifestyle over the next 6 months, like saying no to some social invitations, changes to diet etc.
But, saying all this, it's all worth it as I felt such a sense of achievement at having completed the distance. And yours will be so memorable as you've gotten in to the 'big one'..!
And now I am going to apply the lessons I have learned to improve my time at a marathon next year.
Good luck, I hope that your training goes well, and that you enjoy it!