Hi Aaron and welcome to the Dis! I'm cutting and pasting from my response to a similar thread a few months ago. We really found pushing along as far as we could on the first day made our second day much more pleasant, and gave us a very reasonable arrival time. Since you're leaving from London, you have a few hours advantage over us! As noted below, we found the two Jameson Inns we tried to be clean and comfortable and reasonably priced.
"We used the I75 last December/January and I have to second (third? fourth?) the praise for Dave Hunter's book "Along the I75". For our family (DH, DS9, DD6, me) it was the first time we'd driven to Florida.
For what it's worth, we started out about 6:45 a.m. from Toronto on Friday December 27th and hit Lima, Ohio for lunch and Georgetown, Kentucky for dinner (where the kids changed into their pyjamas). We stopped for the night in Cleveland, Tennessee (just north of Chatanooga) at about 10:45 p.m. at a Jameson Inn, and by this time the kids had been asleep for about 2 hours. The cost was $68, including taxes and a continental breakfast. The total mileage for that day was 1,358.2 km. We lost some time that day with a rush hour delay in Cincinnati, construction, and a prolonged lunch stop.
The second day we hit the road at 6:30 a.m., stopped for lunch just north of the Florida border, and drove up to our WDW hotel at 6:09 p.m. (956.2 km, for a total distance of 2,314.4 km). Since it was a Saturday we had lighter traffic, even through Atlanta.
We definitely liked the idea of driving further the first day and having an easier second day. The book was helpful in telling us, for example, where we could find an exit with both a McDonalds and a human fast food outlet for the adults. It also helped with finding name brand gas stations and suggested Jameson Inns as being clean, reasonably priced and reliable. (We found that to be true, and also stayed in one on our way home).
We'll be using the I75 on our trip this December, too."
Have a great trip, Aaron!