If you've managed to get the stumps and roots of the trees out, fine, but if not, you'll need to treat any woody remains with a brushwood killer such as SBK - means drilling or cutting into the wood and applying SBK, without spilling it on the ground.
If you had ivy there, its unlikely you've managed to remove all the roots, and treatment with SBK on the woody parts is essential. Unfortunately, this means you won't be growing veggies there till at least next year. The soil will need soil conditioning composts applied to it, but some manures shouldn't be used if you intend to grow root crops. However, the essential thing before all that is to make sure you've actually got rid of all roots which might regrow, either by thoroughly digging and removing, or treating any you can't remove.

Whether the roots will try to regrow depends to some extent on what they are. If you are really dying to get started you could perhaps buy a tray of winter brassica plants to put in right at one side- Kale or spring cabbage. Dig out large planting holes and fill them with good compost. Plant the young plants firmly and water them in, keeping them regularly watered at least until they start to grow. This would leave most of your bed bare as MG advises, but would at least help you to feel you were on your way. It wouldn't matter too much if a small tray of 9 plants didn't do very well, but they just might. You would still be able to work on conditioning the rest of the bed. Purists wouldn't approve, so its up to you really!

I would wait and see what re-grows by the autumn. Dig over again and leave the ground rough for the winter frosts to break down the heavy soil. Dig over again in spring and incorcorate sharp sand to stop the clods of soil reforming.