Sounds like a common issue (differences in rates that is!).
In alot of cases, insurance policies already written cannot re-rate themselves on 'New Business' pricing.
Most insurers will see their rates fluctuate on a daily basis taking into account claims information amongst a myriad of different factors.
The renewal price will often be set taking into consideration the previous years premiums as well as the changes to risk the company has seen from one year to another.
An online brand new quote on the other hand, looks solely at New Business rates and current risk trends to establish a premium.
Then adding the internet discount (as well as the already existent problem of retention due to a competitive market) into the fray often makes policies cheaper.
The insurance company is not trying to fleece you (hard as it may be to believe sometimes) they are simply unable to tell you what your policy would be at New Business without actually taking you through a brand new quotation. They normally won't agree to do this over the phone, thus internet is your best bet.
The best thing to do is what you already have. Get someone in the insurance company to compare both the policy and the new quote. If the company applies common sense - they will simply match the premium and retain your custom. There's no point putting you out as a customer by making you cancel one and set up the other - plus it normally costs them more to do that anyway.
At least, that's my understanding of it. Please correct me if I am wrong.
I'm glad you got yours sorted. It does pay to shop around, even if it's with the same company.