Pre CTRL section 1:
Eurostar would have left Waterloo and gone over the Nine Elms flyover to reach the line from Victoria. It would then go past Wandsworth Road and Clapham High Street stations, before going through Brixton and heading to Shortlands via Herne Hill and Beckenham Junction. From Shortlands it would head through Bromley South, before diverging at Bickley. From there, Eurostar would go through Orpington, Sevenoaks down to Ashford via Paddock Wood. At Ashford, it could either call at the International platforms or 'go round the back' on the through roads. Then on to the Channel Tunnel.
Post CTRL section 1, pre CTRL section 2:
Same as above, except... the trains at Shortlands would go through Bromley South but on the Chatham lines. Eurostar would NOT diverge at Bickley, but instead go through Swanley, before joining the Chatham main line, through Farningham Road and heading towards Fawkham Junction, a spur specifically for Eurostar to join CTRL (HS1) at Southfleet Junction and then onwards as now.
I believe sometimes Eurostar was diverted between Brixton and Shortlands via the Catford Loop.