Update - visited my local Jag guy this eve. After looking around quite a bit, he believes it is the clutch master cylinder. What is disappointing is if it is the master cylinder I had it replaced last July. 
So sounds like you boys are spot on hydraulics wise! I hope that’s all it is! Keep you posted.
If its not one thing its two others…
What about the slave cylinder ?
He didn’t mention it. I don’t know if this helps diagnosis-wise, while the car was up on the lift I was in the cabin and would pump the clutch pedal when he asked. Eventually the pedal was close to the floor with no travel and shifting was not possible. The fluid he extracted was cloudy which he stated is a sign of a worn seal.
Just my 2C but if you’re going to replace the clutch M/C I would replace the slave and hose at the same time.
Furthermore I would send them both to Apple Hydraulics, they will sleeve them with brass and completely rebuild them.
I agree, false economy to replace only one if they have been in service for the same length of time.
I’ll call the mechanic today! As an FYI I did view the slave cylinder with him and he felt that it looked new or at least recently replaced.
The slave only has one seal, and it is to the outside. If it goes bad and leaks, there will be puddle on the ground, and it will drain the reservoir. A leak was not reported. Yes, it is possible for it to leak air in, and not fluid out, but unlikely. One reason is if it can leak air, it usually will also leak fluid, but also because air leaking into a hydraulic system like this usually requires a suction action, such as the quick return of the master cylinder piston sucking fluid back from the slave. In this case, the pressure plate pushes on slave enough to prevent that from happening. Unless maybe if one slips their foot off the clutch pedal and the pedal flies back. Also unlikely since there is not enough room on an E Type to slip one’s foot off the pedal. 
Hopefully Salvi has the solution to his problem. As I stated in my previous post, I am not surprised the hydraulics being the issue. I am surprised it was not evident in the clutch pedal feel. But they are all different.
As to replacing the slave anyway. It will not hurt. If it was more than five years old, I definitely would replace or rebuild. Less than a year, it is a toss up.
Tom
This is the exact problem I have. When I stop after a fairly short drive , drop back to second ok , but then can’t get first or reverse or any other gear. I switch off the motor , put into first or reverse and away we go as normal
Well
If the clutch slave is new and bled
And the transmission shift OK until hot
And we have no clue of history
I would be leaning towards a slipping clutch disc or so worn out it slips and doesn’t grab the gear when hot.
Does your car whine when hot from the transmission?
Do you hear a skating noise when hot if you push in the clutch pedal if so
Well you need at least a new clutch and throw out bearing
As wiggles would say…
Eeeeengine out!
Gtjoey1314
At the risk of repeating myself…
When a bit of air gets in the clutch hydraulics the problem first manifests itself in the selection of first and reverse.
It is often gets worse as things warm up.
It can sometimes be temporarily overcome by rapid pumping of the pedal (compresses the air)… more useful as a diagnostic than a driving style.
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Hi Andrew
You problem may be that the clutch is not disengaging enough and that cause could be a very worn clevis pin fork (where the Clutch Master Cylinder pushrod meets the clutch pedal.
This problem is more pronounced when the engine is warm as the synchro rings have more friction to synchronize (and overcome the problem) when cold than when warm (my theory)
A test for this is the following.
With the car transmission fully warmed up (a good half hour drive or more) and idling in neutral with the clutch engaged (out):
press in the clutch
count to five seconds
then pull into reverse gear and see if the gears grind
if it grinds try same with ten seconds
If you have grinding when pulling into reverse as above then try the below
With engine off, car stopped and handbrake on… put your hand on the clutch pedal rubber and see if there is any free play when you try to pull towards the rear of car and then towards the front of car.
I had this exact problem and had about 1 1/2 inches of free play due to a worn clutch clevis pin fork. Synchro rings wore out (in first gear most of all) and engine had to come out. I had a machine shop weld the clevis pin fork up and drill a new hole in the proper place for the clevis pin.
Do tell us what you find!
Dennis
69 OTS
FYI - my clutch master cylinder and slave cylinder were replaced on Monday, so far so good! Fingers crossed.