There have been some good suggestions already, keep the spare wheel run with 50-100% fuel so extra weight on the rear (you are not racing, and if you get near to those speeds you better be insured).
One very important thing in my book is to get the car up on stands and do a nut and bolt check on all the suspension and brake parts, ie. spring hangers to the rear axle, all suspension joints, top king pin nuts etc.
For any trad Morgan the 2 upgrades that help with handling are Panhard rod and Brake Reaction bars, these will help greatly on the day, but not completely necessary.
Like others my advice is get at least 5 laps with an instructor to guide you around the circuit to spot braking points, apex and exit points. The key to it is smoothness the more you unsettle the car the more unsettled you will become, and erratic as a result.
I went out a few years ago at Castle Coombe with a chap in a Datsun 370Z, he kindly invited me, initially I felt rather uncomfortable as it was on of the brakes with the car lurching about the track. I asked if he had much track day experience, his response was no first time. So I suggested he backed off at least 10mph, took his time braking into the bends, selecting the right gear and gradually accelerating out. He did so and with in 2-3 laps everything was much calmer, I then suggested he gradually increased the speed which he did, the result was he lapped quicker and smoother and he felt in control.
