The short answer is no! That's because you may get an offer if you phone in or you go online and see what they can offer you. I think the monthly fee will be £6.50 but the cost of the box itself in ie installation can vary depending on what they will waive for you. Check online or phone in.
Firstly I'd like to welcome you to the forums, and thank you for your post. To answer your question, I can't give you a specific cost of this as it would depend on the package that you already have. The best thing would be to give us a call on 150 or 0345 454 1111 where once we pass security, our customer service department can give you a no obligation quote.
However here's a rough estimate, as you already have an additional box, which you want to change over to a TiVo®, you could already be charged for an additional box, so this would mean an increase in your monthly cost by £5, and if you chose the TiVo® 500GB box then you could get this via our QuickStart service for just £9.99.