I dont know the experience of others, but my car is not driveable until completely warmed up (as in for 10 minutes) - spits back etc.
Once completely warmed up, its fine, but it is extremely slow on takeoff.
Then, once moving at 20mph or so, it rockets (even squeals tyres into 2nd gear (its auto)- its then very fast.
Some kinda rapid acceleration from standstill would be nice!!
Are Mk2s normally sluggish from standstill?

 

Mk2s are far from sluggish at pull away. Your problem may be related to being so over carbureted.

 

Oh. Mine wouldnt take the skin off a rice oudding from the traffic lights then really does go like a rocket. On here, someone did suggest that it was all a bit much. From my understanding, E-types had a similar set-up so I wonder what the difference is

 

I think you will find it is down to fine tuning the carbs. A case of too much fuel at low revs causing the spluttering then enough at high revs hence the better top end. Try weakening off the mixture on each carb and try again, and again until you get the right fuel mixture at the right RPM. I had a similar problem when my engine was cold and I was running it on the starting carb. Would not pull away at low RPM in the winter which did not help as it to was an Auto so you could not drop the clutch and feather the throttle as you can with a manual. Once warm and the starting carb was off I did not have a problem. I solved it by warming the car up on the drive with the AED on until the car was at running temp and I could turn off the AED. Fine adjustments overtime with the carbs using a colour tune kit sorted the problem and I am able to drive the car normally now summer or winter.

 

Almost certainly an incorrect air-fuel mixture. Could be rich, or could be lean, either would do that.

You also may not have needles appropriate for the carb/engine combination, as you can be lean at one point in the load range and correct in another. My guess is you are lean at idle, and closer to correct at higher load off idle. A modern wideband AFR gauge ( I really like the AEM brand) and a tailpipe clamp to enable temporary use of the meter without having to weld a bung into the exhaust will tell you everything.

 

IIRC ~ The first Automatic E-Type built was in 1966 onward, 2+2 model only (Long Wheelbase) & the Series 3 introduced in 1971, Available with the new 5.3 L Jaguar V12 engine.