Back in the '80s P&O operated a Boeing hydrofoil between Tower Bridge and Ostend, with a coach link to Brussels. They called this their 'Jet Ferry Service' and one of its problems was the water intake used to ingest plastic and other detritus causing engine failure.
My broking company at SEN used to be contactable on a 24 hour basis by P&O and many is the evening when I had to hastily arrange a 737 to position into SEN to fly the stranded pax across. TEA was the operator of choice as they seemed to generally have good availability at short notice and we never let P&O down by failing to come up with an aircraft. We obtained the contract only because P&O's internal travel agency wasn't very good at finding a cost-effective charter - they used to favour Laker 707s out of LGW at twice the cost of our 737 charters.
I'm sure the same thing could be done today, but the corporate culture now tends to be to cancel the service and wash your hands of any moral responsibility towards your pax travel arrangements.
I agree that the numbers of pax involved on Eurostar services would make an 'airlift' operationally more difficult to achieve.