I went through exactly the same situation since after getting my master’s degree in Mechanical Engineering I worked in the energy and engineering sector for almost 5 years in a Belgium/French Multinational company. After that I did a 2-year MBA at IESE and then joined McKinsey where I currently work.
To reply to your question, nowadays all the big management consulting firms (MBB, AT Kearney, RB, etc.) are not only global but much bigger than years ago and as consequent of this they created inside them specific departments covering any type of industries and functions, including the one you mentioned in the question.
So there isn’t a management consulting company specialized only in the infrastructure, capital and real estate sectors but all of them deal with those projects and therefore my suggestion to you would be, when you will apply to one of them, to express your interests and they will consider you for those specific positions.
More specifically, in McKinsey there is a practice called Operations where one of the main branches is called Capital and Infrastructure Projects. In the operations practice they did a lot of implementation projects and are full of consultant with a strong engineering background and you can certainly find there the type of projects and activities you liked the most. So if you apply for McKinsey Middle East or any other office, you just need to tell them that you want to enter as consultant for the Operations practice, and this is it!
Hope this helps