When doubling Internet connection speed, will my effective in-house bandwidth also double?
If you increase your WAN speed, your WiFi will stay the same bottleneck it is now. To improve speed "in the furthest corners" you need to improve WiFi connectivity first.
Your water tap is somewhat clogged. It won't matter if you double the cross section of the pipe to the waterworks, until you fix the tap. Similar situation.
Just for clarity there are two links / connections here, not one:
- From your ISP to your house.
- It has bandwidth of 40 Mbit/s
- From your router to the WiFi device(s) "in the furthest corners of your apartment"
- It has bandwidth of 1 Mbit/s
The bottleneck here is link #2.
Doubling the speed of link #1 will not affect link #2 at all, unless you reduce it to less than the speed of link #2 (at which point, link #1 will become the bottleneck).
Think of it like pipes (as per Kamil's answer), or roads...
A highway / motorway might have 3 lanes in each direction, while a back road will have one lane for both directions with passing places. You can't get more cars down that back road by making the motorway leading up to it larger.
In this situation you want to look into moving your WiFi access point (often built into the router), or if that isn't possible, look into getting WiFi range extenders. Another option could be to purchase high gain antenna(s), but please check that the router or device has removable antennas first.
You could also look into using Powerline adapters and a WiFi access point to provide a more localised service at the far end of your appartment.
If the 40 Mbit/s connection is adequate for everything you need, there is no reason to upgrade that link - it won't help with this problem. If you have been advised that it will help, then unfortunately that advice was incorrect.