London->Dublin and the CMWC's

David Casanova K
Heathrow to the city via the Tube? Don't do it.
My recommendation will be for the Heathrow Express. And I believe that they will take the bike.

Bikes on Tube? Forget it.

Nah, the Heathrow 'Express' is £25ish return.
Get the Heathrow 'Connect' which stops at a couple more stations, is still fast, will take bikes and is only £12ish return.