The main question might be, 'why would you want to?' as even with a small area of actual soil it would do so much better.
The Bramley like most apples can be grafted on to dwarfing rootstock which reduces the vigour of the tree, but as Bramley apples (cookers) are two to three times the size of dessert apples, restricting the tree to a container would probably reduce the size and amount of crop.
I would guess that you could do this with a very large container which you feed and water extremely well. To get best results you should use drip irrigation with water to which feed has been added when the fruit is developing, as done with professional orchard trees.
But as the Bramley is a much larger and more vigorous tree than most apples, I think you'd find it quite difficult.
I'll be interested to see what others think.

My immediate reaction was 'No', Bertie. My reasoning was the same as your last paragraph - Bramleys are (or can be) such large trees that they wouldn't appreciate being contricted in a container.

We had a Bramley on dwarf rooting stock and it wanted to be a big tree as Spritz says. It grew and grew but did not fruit well. It has been replaced.

Clone 20 Bramley is 20% less vigorous than the normal form but even this on M27 is stillbigger than average. As above, plant in the ground. You have a restricted life span in a container anyway, no matter how much you feed!