Hi,
Unfortunately, I won't be of much help, but I just wanted to share our similar experience. We are actually going through the exact same process at the moment. I am the USC, but I will get dual-citizenship this summer. We started the Green Card process for my husband (UKC) over a year ago, so we are a little further down the line in the process than it seems you are.
I can tell you that you definitely do not need your tax info for the petition. We filed the I 130 ages ago and (like your husband) I have not filed US taxes since I've arrived in the UK three years ago. We have finished the DS 260 as well, and I can tell you that you do not need tax info for that either.
However, our next step is sending off the "applicant readiness for interview" form and then attending the interview. Tax documents are listed as being a document you need for interview. My problem is that I haven't made enough money to be required to file US taxes for the past three years. I have been told that I simply need to put this in writing in lieu of back-filing the taxes and then only file for the current year.
It would be great if someone else could jump in with their experience as I am unsure if the info I got was correct. I might just back-file to be on the safe side. There is an IRS division of the US embassy in London where you can get info (they are the ones that told me to just file the most recent year, but that is because I didn't make enough the previous two). They have a phone service from 9am to noon Monday-Friday at 0207 894 0476, but I think the division might be closing soon if they haven't already. Also, I have e-mailed the London embassy on several occasions and they are really helpful. Good luck with filing.
Kathryn