I think the advantage of the Redhill route was that it could have used existing railways and then picked up a route broadly alongside the Surrey section of the M25 through fairly open countryside.
It isn't as clear to me that there is as obvious a route through the east and north side of London that would be as easy to use existing routes. Of course, four tracking HS1 could have been an option but the gradients for passenger trains are likely to be less of an issue than they would be for freight.
It wasnt using existing railways - it couldnt as it was piggybacking lorries (ie the huge lorry shuttle wagons through the Tunnel)
My first choice corridor (ie with no geology/planning rules thoughts) would be to go under the Thames East of Tilbury, dropping off London trains, picking up Gateway ones, then a big Sweep round Cambridge way picking up Felixstowe, then splitting with one branch going to the Midlands distribution centres and one branch going north to Doncaster area before going through the Pennines to Manchester/Merseyside, enabling a cross Pennine intermodal operation.
As you can see I dream big! The line could be more twisty as not HS but the NIMBYs aren't going to like mile long freights rumbling/whooshing by! And there is the small matter of funding.....unlike the Swiss the traffic is ending here so we can't tax lorries to pay for it without making ourselves deeply uncompetitive.
But just imagine taking millions of trucks off the M2, M25, M1, and M6......