I read the last similar thread with interest, but my situation differs in several ways, so I'd be so grateful for advice. I always write posts that are much too long so I'll try and keep it brief, but happy to explain if needed..
I'm in my mid 20s, single mum with a 4yo. My DDs dad was abusive and doesn't see her. I graduated last year, and currently work in a startup which has given me so much experience but there is absolutely no chance of career progression or a pay rise, ever. My salary is low, but I like and respect my boss and am really grateful for him giving me a shot, especially in the unusual circumstances I was hired.
I live in a city which is almost as expensive as London, but has none of the career opportunities. It's a 2 hour commute each way.
I first properly looked for another job last weekend due to my being pissed off at not getting paid on time yet again (though I always keep an eye out for things in my area), just to see what was out there elsewhere, and found a grad job which required no experience, but pretty much all of the tasks listed are things I already do in my current job. The office seems young and fun (though I’m very aware that a single parent in a new city has little opportunity for non-child related fun and I can absolutely live with that). I applied Sunday night and Monday morning the recruiter got in touch with me, seemingly really keen.
It mostly appeals for the decent salary, the development budget for each staff member, and the scope for career progression. Also the work seems interesting and I'd be very comfortable and confident that I could exceed doing it. I’ve searched hard, and I can’t find that anywhere near where I live.
I have always loved London and my favourite days are going with DD to new, interesting places. The idea of taking her to the science museum, or the history museum or Tate modern etc for free whenever I like actually gives me butterflies 

I couldn’t commute, it’d take too long and cost too much that I would be more skint than I am now. I’ve had to move my dad into my poky 2 bed to afford to live. It’s squished and I love him but he’s really messy/ unhygienic and there’s not enough room for us all. He’s cool with us moving, he'd miss DD desperately but has a friend to move in with, and just wants me to be happy and then ok for money so is hoping I get the job.
So.. I’m sure this will be controversial, but my starting salary is 30k, so about 2k take home, and if I moved I'd get an estimated additional 1k universal credit. I know that’s really generous, but I’m mainly moving for the career progression and am planning to work my arse off to make sure I contribute to society’s ‘pot’ in the long run. I’ve been at the mercy of in-work benefits and their random reductions, overpayments and suspensions for years and it’s made me literally suicidal; I dream of being without them (though am obviously appreciative to life in a country where they’re awarded). Annual promotion is typical within the company, and each staff member has a generous development/ training budget which they can spend as they wish.
So that’s 3k a month. My office will be near Shoreditch. I’m scared about finding DD a school, but apparently 2015 was a really low birth year and though the borough I’m looking at doesn’t publish primary intake data, neighbouring boroughs say they have over half of schools undersubscribed.
I’ve found some nice enough flats for £1500. Though I don't know the areas, so I'm going to commute for a month and scope out which ones are too stabby to consider.. I’m estimating my bills to be £500-600. So that leaves me £900 for food, petrol, treats, savings etc. So so much more that I have now. Does this all sound about right to any Londoners? I'm pretty streetwise, have grown up in a not nice area and am not expecting Notting Hill, but I don't want to live anywhere we are at serious danger of getting hurt obviously.
Atm, even with my dad chipping in for bills, my income is barely more than essential outgoings. With my DD sharing a room with me, and a fairly long commute with absolutely no scope for career progression.
The lady in the other thread was overwhelmingly told that she was crazy to move for 55k, a little more than my gross salary (I’m told I can expect bonuses etc but obviously my universal credit will reduce due to these). But I’m desperate to be free from benefits, and to be successful and build a great life for my DD. There was 4 of them, they already had a nice house and life up north. There's just 2 of us, and we're barely surviving.
I haven’t got it yet! But it’s all progressing very quickly and they seem very keen. That wasn’t short at all! But am I mental?