Hello
I worked for an agency for a little while in SEO and i can tell you the people getting in the business weren't always good at explaining the full truth to customers when it came to SEO. Which upset me greatly.
Can you maybe explain more where this duplicate content in? I am a bit confused by your link. I would also agree with the other person who has answered. Simply changing your logo shouldn't result in such a drop in positions. What i would suggest it could be is bad backlinking. The reason i say this is because the Agency i left had no SEO person for 6 months after me. All sites were doing well then after i left they just anyone to just do the SEO. This resulted in people constantly link building to sites that were no good. Then one company crumbled in the SERPS their traffic dropping for 10,000 a month to about 2,000 a month in what should be their busiest time. A friend of mine who worked there still kept me up to date on the situation told me their rankings went from page 1 all the way back to page 5 for keywords they had ranked highly on for a long time.
I believe their only option in the end was to take down the site and relaunch on a new domain to break the links with the old bad sites. I believe they seemed to have picked up in traffic slightly.
So in answer to your question this could be the problem. Duplicate content shouldn't cause such a drop. However, surely your SEO company should be making sure there is no duplicate content? As for the phone number i haven't heard that before. If it is in the header or the footer, i shouldn't think it will make much difference. AS there are plenty of companies out there that have the same registered address but are different companies. This info is on the website in the footer normally and their websites are being penalised.
They want to charge you £1250! When i worked in an Agency it was about £40per hour. When i do freelance i charge 20 per hour. Based on those figures they say it is going to take 31 hours to fix!! As i assume you will have to pay VAT on top. I am not sure how they can say 31 hours is the amount of time it will take to fix. What are they going to be doing on it? I would demand a breakdown of exactly what they are doing for that money.
Also can you confirm if both sites are selling the same products or to the same market place?
Hope this helps.