He expected there----more room for him to put in a desk

B.
expect vt.预计...可能发生(或来到);预料;预期[+(that)]或者[+to-v]
如He expected to finish the work by March.他预期三月份完成这项工作。

这里是there be, 就变成了 there to be

如果是A的话，则是省略掉了that, 但是应该跟expected一样用过去时would be

B.
主句是过去时态，从句应该用过去的时态
排除A

选择B。