Sorry to hear about Anthony's tale. It's a good lesson for us all to learn. Never have blind faith that the other party will make the right call, or do the right thing by you in the end. They probably won't.
I've read everyone's thoughts on the right way to be an indie. I think there are several methods, and you have to find the one that works for you.
After Uni
I actually think graduating and having a bash at being an indie is a good time to do it. If you move back home with your parents after uni and they're willing to support you, it's a perfect opportunity. No financial responsibility. It's the only time in your life you'll be free full time and not be tied down with financial commitments (unless you go to prison!

). You can use the "gap year" excuse to employers if you need to get a job in the end, and that'll be fine. The only problem is, will you be mature enough to commit to full time self motivated work? 90% of people won't imo. I tried it. I wasn't!
In Your Spare Time
The idea you can create a killer game in your spare time around a full time job is a bit of a pipe dream to me. It's just so much of an undertaking to work all day, then all night. A few hours during the week and then a day at the weekend is not enough to make anything other than a simple PC or mobile game. You may get lucky and hit upon that formula that succeeds even though you hardly put any time in, but to really have a good chance, you need to put in a lot of work/content/awesomeness into your game, and for that you need a lot of time and effort.
I don't believe this is possible while working. Again .. I tried!

Perhaps if you have no other hobbies, no friends/social life and unwavering determination, it's possible, but for 99% of humans, I don't think it'll work.
Save Up
So the other idea is that you can save up loads of money in employment, quit your job and do it full time. This is a more realistic solution in terms of having realistic resources/time to do it, but it's still highly unlikely. I don't know anybody who could save enough money to support themselves, pay the mortgage etc. for 2 years without working. The really well paid may be able to, but I think they're less likely to want to. If you're earning £100k/year, but living in a modest house, do you really want to give up your £40k of disposable income and your good job on a high risk job which will never make you as much money (unless you're extremely lucky). I just can't see anyone ever doing this realistically.
Get Sponsored
If you're really lucky, and someone believes in your game, or you manage to convince people on KickStarter that your game is worth paying for, maybe you can get some finance. But can you get enough? And are you still willing to quit your job and risk it all on your game idea that may not come to anything? I think this is a more realistic scenario than the "save up for 2 years" one. Perhaps you can combine the two, save up some, get some sponsorship (in exchange for a percentage cut), and maybe some kickstarter money too. Then you may be able to survive for a year while developing, but the risk is still great if you leave a good job.
Marry Someone Rich
The last solution is to shack up with someone who can support you while you work on your business. Dream scenario! Aim for this!
As for the making money from mobile games method, I wouldn't rely on that either. To be really successful in that, you still have to put in a massive amount of hours to make a game that stands out and has quality. Perhaps you have more chance of doing this in your spare time than a PC title for example, but that's still a really tall order!
Anyway, that's my rant done. I personally think after graduating while living in your parents basement is the only realistic scenario for becoming a full time indie.