Spent tomato potting compost

There is one vital thing to bear in mind there:

1. Spores of Late Blight persist on/in living plant material, either tomato or potato. Are ou absolutely certain there is not even a shred of tomato in the spent compost?

and I know you usually use peat, which has little nutrient value, so therefore spent compost should be fine, but most commercial mpcs are alkaline, which would encourage potato scab, whilst peat is slightly acidic and would give a degree of protection

I wouldn't. but I am sure opinions vary. There are usually lots of different ways of looking at things!

I have trouble with badgers on my allotment plot, and whilst I have managed to keep them off the carrots this year, thanks to a tonne of metalwork, I had a cunning backup plot, so at least we had some carrots for Christmas 

I dug out a trench behind the greenhouse at home, a spade wide 6' long and a foot deep, then filled it with the previous year's compost. In this I sowed two rows about 6" apart and them thinned the plants to 3" apart with the rows staggered.

I have the best carrots I've ever grown, the one in the picture has not even been washed!