I did almost exactly this (one Lisa was not a 2/10) and spared little expense. Pallet air shipping is a method of choice and it's good that it's available to you.
Widgets: extracted and placed in a foam-padded Pelican case, traveled with me in the main cabin in carry-on. Most Lisa OSs will move the heads to the landing track prior to shutdown; if you want to move them there yourself to be certain, you can use
the PARK HEADS function my NeoWidEx utility. Once the drive is turned off, the brake will keep the heads fixed in place.
Lisas: wrapped entirely in multiple layers of small-cell anti-static pink bubble wrap until it completely filled the interior of a double-walled cardboard "inner" carton (about 1 to 1.5 inches on all sides). This carton went into a sturdy, larger cardboard "outer" carton, big enough for three inches of gap on all sides, all of which was filled with packing peanuts. I cut shielded (no access to inside) handholds into the sides of the outer cartons to encourage shippers to lift the box in the way I preferred. Moving one of these boxes was a two-person job. Double-carton technique is inspired by the way glassblowers ship large art pieces.
ProFiles: same bubble-wrap treatment, then stacked in a larger box with thick foam padding between and all around.
The boxed Lisas and Profiles were crated by the shipping service in a single large chipboard crate fitted with stick-on tilt and shock indicators on the inside, secured with screws and one (monster) wraparound metal band.
It might have been overkill but everything arrived safely! The only hitch was UPS Air Freight, which was more or less awful for reasons that hopefully won't apply to you. In my case, I also basically had to be ready to receive a large, heavy crate, which I wasn't for longer than I had anticipated, and so I ultimately had to have the crate dropped off at a self-storage place until I was ready to deal with it. On the bright side, self-storage places tend to have enormous lock-breaking bolt cutters, which can be useful if you find yourself confronted by an unexpected (monster) metal band.
Moving to London or elsewhere? If elsewhere, presumably onward shipping may be a factor; it wasn't for me.