The LR specialist should be using JLR software call SDD, which has the facility to save each diagnostic session, and print out that particular session too.
Test Book was for the older LRs, and isn't relevant for the FL2 at all.

I can't see how a mistimed belt can cause a sensor to fail myself, as there's no actual need to touch this particular sensor whilst doing the timing belt.

There are no lock washers in the diff. The diff bearing which goes noisy is secured by a special nut, which has a pre-applied locking compound.
It's possible to make a mess of doing the pinion bearing, but there are definitely no lock washers.
Are you sure you're being told accurate information by this other garage?

Wow £4k for under £1k of work.
Sounds like you're using the wrong garages to me.

The first garage charged £2.500 and Land Rover charged £1.500 to put it all right? they have put on the notes planet gears as necc due to previously not used a lock washer so nut was not tight and swarf found in oil drained off diff. They basically said as it was not tight it broke apart as we drove! so the cam sensor fault would not be caused by the timing belt being out and the car driving badly/
 
The first garage charged £2.500 and Land Rover charged £1.500 to put it all right? they have put on the notes planet gears as necc due to previously not used a lock washer so nut was not tight and swarf found in oil drained off diff. They basically said as it was not tight it broke apart as we drove! so the cam sensor fault would not be caused by the timing belt being out and the car driving badly/

Unfortunately it seems you're being spun a yarn by both garages. The first was taking the **** charging £2.5k for a timing belt change, and a diff rebuild. That's 6 hours work tops, and no more than £250 in parts. So they definitely ripped you off, as that work shouldn't have cost more than £1k.

The second garage are telling you fibs, possibly to gain your trust.
Trust my, there are absolutely no locking washers in the Freelander 2 rear diff. It's a fully welded construction, with only 1 large nut holding the pinion in place, and 7 casing bolts holding the fully welded crown wheel in position.
Rebuilding the diff is a 2 hour job, which I did myself just after Christmas.

You really need to find another garage, that isn't going to rip you off.
 
I've a few thoughts on this.
First off, it's impossible for a qualified mechanic to time the DW12 incorrectly, as the crankshaft and camshaft are locked in position, using engine specific timing tools.
So if the timing belt (cam belt) is installed 1 tooth advanced, then the engine could still run, but would be down on power. However if the belt was installed 1 tooth retarded, then there's a real possibility of the pistons hitting the exhaust valves, which would bend them, and the engine wouldn't start at all.
As for the cap position sensor being "blown", this is very unlikely as a result of a slightly mistimed belt.
The cam sensor does need careful setting up of the air gap if its removed, but there's no need to touch it when changing the belt.
The cam position sensor can fail, although it's not common on these engines, but if it were incorrectly installed, it would be worn and physically damaged.
It sounds like your original garage is reluctant to take responsibility, and having another garage say their work wasn't correct, will only get their back up.

I'd like to know a couple of things.
Is the car working now?
And, were there's any codes recorded by the ECM?
the car is working fine now the Land Rover garage has repaired it. yes plenty of codes recorded P1259, Po341,Po2eo,po2e9,Po2e8,Po2e1,Po238. They mean nothing to me? but I am guessing it is stating cam sensor faults? what I don't get is we had a full service no issues, belt change and after that and within 15miles of total driving or at the point of getting up speed on the motorway the car started struggling could they have damaged the sensor when fitting the timing belt? if so how? or is this a random coincidence?
 

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