The original battery trays were made of some sort of chopped fibre reinforced bakelite.

Later pads behind the battery were Hardura felt as I show above.
Early pads were just carpet under felt like yours above

The only difference was a Hardura "skin" on the later stuff.

There was also rubberised felt behind the dash.

I am using official Jaguar terms for these materials per the parts manual.

Hard rubber casing, pitch sealed battery tops certainly leaked some acid as they aged. Normally first occurred around the posts & then the cell jumpers.

Genuine Mercedes Benz batteries that are made to their spec by Varta while basically sealed for life still have a gas vent tube attached to their suitable nipple as they are well hidden under covers & filters etc. (they also comfortably last up to 14 years)

 

Out of interest. Do Interstate batteries that fit the lid clips properly fit in the tray?

All the batteries that fit the lid in SA are too big to fit in the tray due to the front indent in the tray.

Many modern batteries have a clamping ridge around them at that point.

Original tray. Cut out for clutch master cylinder on RHD pedal box.

 

The old style terminal connectors from the 1950s and 60s had no rubber covers. The lid may have served to reduce the possibility of accidental shorts.

 

Peter that too is possible but a more suitable material than the very brittle Bakelite. For example the covers in an XK120 are of the same or similar material but very thick. To your point the bonnet hinge when lowered touches or almost touches the (+) cable but that is Earth so it does not matter.

To Glyn's point not only do modern batteries have a vent the Jaguars they go in have a vent tube to ground. Leave the tube off and the compartment the battery resides in will suffer!

 

Indeed the compartment will suffer, The batteries must be vented into the airstream under the car. Especially at modern high charge rates. The Hydrogen gas plus sulphuric acid fumes given off by SLA or AGM etc batteries while charging can cause a hell of an explosion given a source of ignition in a confined space. Battery explosions do incredible damage.

Here is an old original S Type broken & cracked Bakelite lid. They are certainly thick in places. See material thickness at cable exit cutout.