Double deck trains are irrelevant, because a significant amount of services will need to run onto classic lines to complete their journeys for the foreseeable future. There is no point doing double-deck just for Manchester and Birmingham.
The Leeds branch has not yet been abandoned.
Which means potentially 9 formations out of 14......
A modern double deck train can pack 740 people into 200m.
(EDIT: Even a Class 395 only fits 68 people into one of its 20m intermediate vehicles, with no toilet! Even if we just added four of those vehicles into a Class 395 you only get a seating capacity of ~612 permanent seats)
The practical option is to build everything single-deck and to UK loading gauge with low floor for level boarding at every single platform they will ever serve, be they on HS2 or elsewhere. These trains are going to be 400m long. They don't need to be double-deck too. How often is a Eurostar totally full? It's surprisingly rare except when flights are disrupted.
Eurostar is constrained by a long journey time, lack of economic integration across the areas served and the passport and security requirements.
In any case, once you consider luggage provision (which can't go overhead on a double decker) you barely get 1.2-1.3x capacity.
20% is still rather drastic.
You are throwing away a fifth of the potential final capacity of the route to remove.... a six inch change in height from platform into the train?
(From a 760mm platform to a low floor 915mm platform height unit)
That has to be one reason why Germany just isn't interested, unlike regional traffic where people tend to carry less stuff and you can pack the seats in - even then it only gets you about 1.5x.
But this is the UK.
The captive trains
are regional trains.
You really think a 45 minute jaunt to Birmingham counts as true "intercity".
Or a 68 minute jaunt to Manchester
Or even the 88 minute jaunt to Leeds?
The corrolary of HS2 increasing passenger numbers will be a reduction of the luggage requirement per passenger.
People who travel needing luggage probably already travel, you will pick up day passengers with less need of luggage.
EDIT:
HS2 puts Birmingham somewhere near Folkestone, and Manchester someone near Dover.
What is the composition of passengers on those HS1 trains?