I have an entry-level 27.5 mountain bike and I will be moving to London this summer. Since I won't be riding it on trails anymore I thought I can keep the frame and wheels and build a commuter bike or road bike. I also read lots of posts where people suggest buying a proper road bike than struggling with building something that will be mediocre in the end, but I want to keep my frame at least, since I am attached to it.
What parts should I buy on a budget? I must mention that it would be really nice if I can get a 1x10 or 11 setup.