Generate a random password before your trip and print out a few copies. Take one with you and secure the remaining ones. Before you fly through the UK, change the password on your computer to the random one and destroy the printout. When you get back home use the remaining printouts to change your password back and then destroy them.
First of all, even if you're being truthful, saying "I don't know my password" will likely not be believed. Explaining the process you went through to safeguard your password will merely elicit suspicion by a border agent. Why would you go through such pains if you had nothing to hide? And once they are suspicious of you, you will almost surely be detained and have your equipment seized.
Yes, the government might not be able to decrypt it for years, but they still have your laptop, and they are still in possession of your data, encrypted as it may be. So, I ask you, who won this little battle? It sure wasn't you.
IMHO, the only valid approach here is to host everything on an external server, and VPN / SSH into it to do your work. Don't store the connection info locally, and don't store any passwords / keys locally. Make sure no confidential files ever touch your hard drive, even in a cache. Most agents have no idea how that process works, and unless you have a shortcut on your desktop / home directory labeled "connect to home fileserver" they probably won't even think to ask you for any further info.
EDIT: Stupid spelling error. Thanks, recursive.
Why would you not want a camera in your bathroom, if you have nothing to hide?
I merely figured the HN community would pick up on the sarcasm.
So please do not patronize me.
Obviously the best approach is to just not have your laptop.
I think the safer solution is not to travel with hardware you intend to use again.
He was detained for 9 hours and threatened with arrest during that time, but this was under terrorism laws, not encryption laws. And ultimately he was let go (sans equipment).