HS1 does go from Ashford to Eurotunnel. Eurostars use that 300km/h TVM equipped section. There is an old 3rd rail line running along side it for most of that distance up to Dollands Moor - maybe you're getting confused with that?
The Southeastern High Speed services don't use that section of HS1 because they diverge at Ashford and head towards Folkstone and Dover which uses the old track - not the new high speed line.