Attention! This is a list of songs from the re-aired episodes, not the original BBC broadcast. I saw a lot of people asking for songs from the re-aired episodes so decided to list all of them in one single post.
1) 00:30 - Fuzzmann & Whammyboy - Chicken Chokin'
2) 03:20 - Jim Dooley - Ancient Crystal
3) 46:40 - Dweezil Zappa - Electrocoustic Matter (This one I found myself. Its played when the trio are on the ferry in Italy, arguing about where they wanted to go. This part is not there in the above video. I heard this song on the full version on YouTube. I managed to download the video just before it was deleted)
4) 05:30 - John Powell - Full Force (San Bernadino Pass. This replaces Quinn - Acedia (The Noonday Demon) from the original version)
5) 07:10 - Jim Dooley - Mystic Tryst
6) 07:30 - John Powell - Mystic Prelude
7) 08:15 - John Powell - Mystic Prelude (Again. Played at the Stelvio pass intro)
8) 09:35 - Henning Lohner - First? Sight (The last part where Jeremy says 'As the cars ticked themselves cool, we knew our quest was at an end" and lasts till the end of the video)
Thank you to all those who have already listed these songs above. That's how I found most of them. All I did was put them together. Also, I have a request. I need to know the song that starts at 08:00 in the video above. The part where Jeremy says "We had all pretty much decided that we've found the best driving road, well, two of us had". Thank you again!