We are staying near Limehouse DLR. what is the best route via the tube to Victoria Station. On a Monday morning.
Is Victoria Station your final destination or are you going somewhere else from there?
DLR to Bank/Monument and then Circle or District line to Victoria.
Alternatively there's DLR to Tower Gateway, then walk to Tower Hill and then Circle or District line to Victoria.
Barons Court? That sounds like the route from Heathrow, not Limehouse.
Oh, Marco. LOL. I thought OP was going to the Lime House Hotel. Sorry! Where are my glasses?!
PS, I deleted it to avoid confusion. :0
FYI the walk from Bank to Monument is at least a 1/4 of a mile walk. They are adjoining stations but it is a surprising trek if you are not aware of the distance.
And just to be clear you are asking how to get Victoria Station from Heathrow or am I miss reading your inquiry.