Well, I'll confess (as I've done before) that I'm not an expert on older cars. What I'm a bit better at, though, is searching the Web - so I started with the sponsors on the cars' racing numbers and found out that this had to be the Mille Miglia, and when you said it was in 2007 I started looking for photo galleries from the 2007 MM. I found quite a few, and then I found the start list:
http://www.barchetta.cc/All.Ferraris/events-stories/events/2007/rallye-races/mille-miglia/1-mille-miglia-entry-list/index.html...with all the details of model and year. The only problem, though, is that the numbers don't all match - for example, number 4 is supposed to be a Bentley 4 Litre, which we all can see it isn't, 35 should be a Mercedes 630 SK, which it also quite obviously isn't, 68 should be an OM 665 MM, and so on. So I had to look for similarities instead - which is quite easy until you get to a source that claims that a Lagonda is actually a Talbot, as I said (supercars.net).
The official entry list also claims that there were only two Invictas in the 2007 race, and that they were both 4.5 S models from 1931. Which is why I said it had to be one of those. As for the Lagonda - well, that was a matter of deduction: There are only four different Lagondas on that list: The 3 Litre, the LG45, the LG45 Rapide and the V12 LeMans. It was obviously not the green LeMans, neither was it a 3 Litre, so according to the list it would have to be either an LG45 or an LG45 Rapide. I thought it was more similar to the LG45, so that was my guess.
Of course, the entry list could be wrong (but I thought that would be a bit unlikely). Nevertheless, it's quite a fun way to solve a puzzle - a bit of detective work, really!