This isn't strictly true. A lot of the London underground was built first and then housing developed around it. Actually the tube getting to a place prompted massive development in the area. Similarly now if a new line gets created to an area in many cities you see development around it.

The tube was built outwards, not within. It was a reflection of demand for housing that already existed in quantities large enough to justify it, and was also growing at paces never seen before with no end in sight, and there was no possible way to build upward at the time. In other words, given the conditions of their time, they were building the infrastructure in response to already existing demand.

Isn't the massivly rising house prices a reflection of large demand for housing?

There were many ways to build upwards at the time but London favoured single family houses. Cities like Paris built upwards around that time. Even to this day Paris is more densly populated than New York because almost all buildings in Paris are around 7 stories rather than a very tall core surrounded by a lot of single family dwellings.