@vkd In all seriousness, if your Spitfire has as poor of cornering ability as you state, I'd take a serious look at the suspension. The Spitfire, with its pseudo-independent rear suspension(compared to the live axle on most others), had a good reputation in the day for being one of the better handling British sports cars on the road, a type of car that in general is well regarded for its handling rather than all-out speed.
Unfortunately, LBCs often have their tires neglected, and you should probably change them once every decade or so regardless of the amount of wear on them.
Take a good look at ALL your suspension components. Spitfires have a single leaf spring in the rear that straddles the differential. It will almost always sag over time, and in extreme cases will break a leaf. I drove around in my MG for a little while with a broken leaf on one side, and it makes the handling REALLY unpredictable.
Check ALL the rubber suspension components, as rubber is a perishable item and bushings at best are good for 20 years-usually less. If you don't mind throwing a bunch of money at it, neoprene bushings not only stiffen the ride but also last nearly forever-the downside is that they're 5-10x the cost of rubber. I spent about $10 for a full new set of rubber bushings on the rear of my car(both sides) and the neoprene set is around $90. Wear in the front kingpins, tie rod ends, and steering rack can all cause issues.
Look at your shocks. In the best case, you may want to top the oil up in them if it's low/missing(an Armstrong shock won't work without oil in it). There's a lot of debate about the correct oil for these-I know a lot of folks who swear by SAE 20 motorcycle fork oil, although I worry about the pressure that an oil that heavy puts on the seals of an old shock. It also gives a fairly firm ride. I use dirt cheap SAE 10 hydraulic oil from Napa, which has is close to the factory weight and gives a good compromise between handling and ride quality. Be sure you clean the area around the fill port before removing it, and work the shock while adding oil to be sure it gets everywhere it needs to go. If your shocks won't hold oil, considering sending them off for rebuild or installing reconditioned units-I'm a big believer in retaining Armstrong shocks where originally installed. Tube shock conversions are available, but pay careful attention to how they attach-I've seen some that have the potential to be down right dangerous if they come lose while simultaneously doing a poor job of actually securing the shock.
Finally, I've seen cars that folks claimed couldn't handle well, and unfortunately I've found that the biggest issue was in the big nut that's behind the steering wheel. There's no a lot that can be done for that, unfortunately.
