You can use 4,500 avios for the train as well
+1
But not so simple.
You cannot redeem BAEC avios for Eurostar.
You can redeem avios.com avios for Eurostar.
Solution
Open an account at avios.com
Move some avios across via Combine My Avios
Ring avios.com to book Eurostar
Move your spare avios back to BAEC via Combine My Avios
Though doubt your tix will be 4,500
Tickets
start at 4,500 each way.
Adult Standard return
9,000 Avios
6,000 Avios + £30
3,000 Avios + £50
Child Standard return
8,500 Avios
5,000 Avios + £20
2,500 Avios + £40
Adult Standard Premier return
26,500 Avios
16,000 Avios + £70
8,500 Avios + £120
Child Standard Premier return
20,500 Avios
12,000 Avios + £60
6,500 Avios + £90
Examples are
starting prices and are subject to availability. Exclusions may apply.
Btw, Amex Plat should get you acces to the Business Premier Lounges on both ends.
This is all info pulled off various threads on FT.