I would say you should definitely try submitting to London first. I don't know if it helped that I changed to a spousal visa, but if they based it purely on the amount of time I've been in the country, than they're sure to accept her I-130 petition. Check out this link
http://london.usembassy.gov/dhs/uscis/i130filing.html (ignore the bit about ILR) and look at the checklist link under "How do I file the petition?" Have her include a cover letter requesting that the petition be returned directly to her if they're unable to take it so that the correct form of payment can be added. London USCIS takes credit card but the US service centers do not. If they accept it, you'll see the card charged within a few business days and should probably receive a postcard with your receipt date although not everyone does. The whole process should take about six months to gain you a CR1 if you've been married less than two years at the interview or a IR1 if you've been married more than two years by the interview. That is definitely the ideal route. Saves time, money, and headaches.
Unfortunately, yes, you will definitely need a joint sponsor unless you want to wait in the UK while she lives and works in the US for a while alone. Or unless you have huge assests, totally something like three times the yearly requirement I think. I haven't seen the official word on that, but I have heard others talking about it. I believe the 125% figure comes from the I-864 form, which is the form that the sponsor and any joint sponsor fills out. If you go the London route, this form has be completed by the interview date. She has to fill one out as she is the main sponsor, even if she's reporting zero income. There might be some confusion with not having filed taxes in the US the past three years, but hopefully someone else can give advice on how to prove that she didn't have to file. If she made any money in the UK, she'll find it best to look into how to back file taxes. The US Embassy in London should be able to help her, or even the IRS helpline. Don't worry about her owing anything though - she'd have to make more than $82,000 USD in the UK in one year in order to owe the US govt any money. As long as she's been in the UK 330 days of the year for each of the years she's been gone, she's fine.
The joint sponsor or sponsors don't have to be her parents. It can be anyone who meets the guidelines willing to fill out the form and agree to cover your back for 10 years or until you become a citizen. I think they're only liable if you actually have to claim welfare or something, so really it's just a matter of forms in your case.
The forum at www.diveinamerica.com is a great place for US/UK couples who are filing in London.