IO540 "I don't know how Heathrow used to handle that..."
probably in the same way that they are as of right now - they are still fully operational, despite anything you, or AFPEx, may say or think to the contrary. IIRC, didn't you say previously that you've never used Heathrow FBU?
VFR Transit - file your FPL just like IO has suggested, or, if you are within Heathrow's area of responsibility, maybe give them a call and file it yourself over the phone? The 'present means' works very well, thank you very much!