S&S couplings are the answer (granted, not a cheap option) which means that getting a tandem into an estate car is doable. We've got to the point where I can get ours into or out of the car single handed.
A couple of years ago, my brother in law rang on a Saturday morning to ask how long our tandem was: he worked for Scotrail and they were trying to estimate whether they could permit them on some of the local trains west out of Glasgow. We told him, but suggested he should hire one and try getting it on and off at the various stations, with video of the attempt: he didn't take us up on that. Which was a shame, it would have been fun to watch him try...
We have in fact managed to blag our way onto trains, usually by saying 'it comes apart - we can dismantle it once we are on'. Sometimes we even do that. But UK trains are generally unfriendly, unlike one Belgian one where we stashed it in the lobby, and each time the ticket collector came round he happily stepped over it without the slightest complaint.