bluerach, I could almost have written this (although my son has so far mostly stayed away from the police, except when I have called them)...
I tried the 'no money' approach. I stuck to it for over 3 months on 2 separate occasions. It didn't work. Here are some of the things that happened when I did it:
He stole from me as often as he could manage it. I bought a cash box and had locks fitted to bedroom doors :( but frankly I wasn't able to be infallibly vigilant and there were always opportunities (for example, when I came home from work and rushed up to the loo... When he was out and I thought I could relax, but he came home...)
Once the 'stealing taboo' had been broken, he started to steal other things from me too - especially alcohol but also some 'treats' I bought or was given, like mothers' day chocs :(
He sold all sorts of things: DVD player, DVDs and computer games, my old mobile phone, my bottles of alcohol, hoodies, trainers, gift cards he got for Christmas...
He took money I gave him for fares to college and for lunch, didn't go, and used it to buy drugs instead.
He borrowed money from friends and 'paid them back' with items like DVDs and computer games, or with alcohol he stole from me.
He relied a lot on good will: his friends supplied him with drugs on an almost-daily basis. Because they are mostly young and their access to cash is limited, there seems to be an acceptance that everyone will be 'broke' sometimes, and if someone gets stuff free from his mates one day, that person will be in a position to 'pay it back' sooner or later.
He gained access to my savings account without my knowledge, and stole around £850 from me over a couple of months (presumably paying back all that 'good will') :( :(
He had been doing chores regularly for cash. When I withdrew money, he withdrew his 'labour'. He refused to do anything - even put his own dirty plates in the dishwasher.
He also had various attempts at 'bargaining'. He refused to go to school/college unless I paid him (his attendance plummeted), he refused to communicate/let me know where he was, etc...
I had no 'leverage'. Money is a big motivator for teens, but I could no longer bribe him.
We then got into a bleak spiral of ill-will and punishment: since I could no longer withdraw or restrict money - because I had already - I blocked his phone (I pay for a contract), stopped buying clothes and withdrew my own labour (no washing, no lifts, etc.), but that was about all I had left. It was horrible.
He had a sense of 'entitlement' and 'victimisation' - I was the mean, evil mother who wasn't giving him what was his by rights ("Everybody else's mum gives them...", "No-one else has to do jobs to get money...", etc.) so he was able to justify all sorts of bad behaviour and unpleasantness.
He was constantly angry with me (and I have to say the feeling was pretty mutual)... There was a lot more crashing and smashing and swearing. I had to call 999 on 3 occasions. :(
SO... I re-introduced money... While it was still term-time (he's finished for summer already
) I gave him £4/day - £2 for bus fares and the other £2 for lunch or whatever else he chose to spend it on. I now give him money for chores/jobs/attending college/effort. If he doesn't work, or doesn't make an effort, he doesn't get any.
I still have other safeguards in place: I keep money and valuables locked up. I do not give him money for clothes - I take him shopping...
He now also has a small part-time/casual job, so he has some independent income anyway... If he'd had that a couple of years earlier, all my other efforts at controlling his behaviour and drug use by controlling his cash would have been impossible 
Ultimately, I feel withdrawing money didn't work to stop him taking drugs, and led to some other very undesirable behaviour as well; whereas giving him some money as a reward for effort is at least encouraging him to do some work, he doesn't 'have' to steal, his behaviour is a bit better and more settled, he is more motivated to go to college, and the anger-levels in our house are lower.
Btw, I am pretty sure I remember Maryz saying she gave her son money too, for similar reasons... So it must be right! 