I had to dig out an old book on channel tunnel to check this, so unless signalling has been altered, then the TVM430 sections in the tunnel are around 500m apart, much closer than on French high speed lines.
If a train does 120km/h then will be fully unrestricted (5 clear signal blocks) every 2.5km which takes 2.5 minutes. At 4 blocks will get advance caution (sort of equivalent to triple Amber signals), get closer then more restrictive speed, with a do not pass (effectively red signal) with one complete block protecting rear of train ahead.
But the high speed passenger trains run faster, upto 160km/h for the passenger trains (the book actually says designed to allow 180km/h but normally restricted to 160k/h for pathing).
It says can put 18 trains an hour through, but the extra paths would mean the high speed services would need to follow Eurotunnel shuttles, not really a problem for freight trains, but fewer minutes slower to traverse the tunnel than the faster (160km/h path)
So, can take more trains, but it takes a few minutes longer. The extra time is probably similar to adding a stop at Ashford or Ebbsfleet. Not a technical restriction, but a commercial decision about journey time.
There is another twist, the French are gradually upgrading their Ligne a grande vitesse to raise the top speeds from 300 to 320 km/h (doesn't affect sections with slower restrictions, 270, 220 km/h etc). They haven't yet done LGV-Nord because of number of legacy second generation TGVs using it which have top speed of 300km/h (those built 1989-1996, eg, Atlantique, reseau, Thalys PBK, Eurostar300 etc). But these are generally being withdrawn within next 4 years. So once slower trains are out of the way would be able to save about 3 minutes in France.
Wow that's some detailed information, thank you!
Today there appears to be a le shuttle service every 30 minutes.
If we were to assume a shuttle service increase to every 15 minutes, plus an hourly freight path, you could do something like (departure times for Eurostar/Virgin/Trenitalia services from StP):
.01 Eurostar/Virgin/Trenitalia
.04 Eurostar/Virgin/Trenitalia
Shuttle service immediately following above
.16 Eurostar/Virgin/Trenitalia
Shuttle service immediately following above
.31 Eurostar/Virgin/Trenitalia
.34 Eurostar/Virgin/Trenitalia
Shuttle service immediately following above
Freight service immediately following above
Shuttle service
That should leave enough space for all the Eurostar/Virgin/Trenitalia to run through the tunnel at 160 km/h.
If you need more capacity for the shuttle, run flighted shuttle services, especially in the second half of the slot.
If somehow 5 tph isn't enough for Eurostar/Virgin/Trenitalia, you could add an extra flighted service (e.g. .37 or .19 from StP, though that would require some timetable changes). However, as raised in my previous post and by other people, 5tph gives a bonkers capacity already. With higher capacity trains coming in (Eurostar's new trains will fit 1000 people Vs the current 750 (e300) or 900 (e320), so there is space for a lot of growth.