Hand luggage x-ray machines will fog film. The faster the film the more likley you are to see it. With Ilford FP4 I have seen it after 3 passes through machines (UK and USA). The effect is cumulative and more noticeable on exposed film. Never put film in the hold. The x-ray machines used for hold luggage are much more powerful and will fog all film that goes through them.
I would expect that if the Xray machine is fogging FP4 film, then the machine should have been retired 20 years ago. Early XRay machines simply used as much Xray as they could get the machine to produce. This had two side effects, one is that it would literally cook film, and two that it would require a lot of shielding in the machine itself. The next generation of machines were adjustable, which meant that if the operator was good, they would set the machine only as high as to get a good image on most luggage, then hand inspect the few that it had trouble with. Some operators were lazy and would turn the machine up to maximum, then refuse to hand inspect anything, a lot of film got ruined because of this.
Just like film is getting more and more sensitive, so are xray machines. In most countries technology goes the same way, a major airport like Heathrow is likely to have mostly newer machines, the older machines from those airports go into slightly smaller airports, and as the machines get older and older they move into smaller and less important airports, until you get to some little airport, where they ring up the manager a couple of times a week to go turn the lights on, and warm up the machine, which has a plaque on it that it was built in 1975.
Another option, if you will be staying at a hotel, is to arrange with the hotel to receive a package for you, and send the film via courier. Check with the courier to see if they X-ray stuff, those that do, will have an option of marking an item not to be X-rayed, film is not the only thing that can be ruined by X-rays. You want the customs papers to state that it is photographic film for your own use and that you will be exporting it at the end of your trip, so your not charged customs duties.