Ok, I understand. I tried many time the 25kph but it's really not for me. 40 kph is the right speed for me, especially when I'm commuting and that I just want to arrive work as fast as possible. I have a little 250W Direct drive motor I peak at 2000W lol.
So, just to answer your question if you ride conservatively, so around 25-30kph. You should use around 10-12wh/km. For a 10 miles commute, that's around 16km. So you need around 150-200wh/day to commute. Your lipo has to have at least 50% more capacity for maximum longevity, so a 300wh lipo would work fine for your commute.
Just remember that this setting wouldn't allow you to go out anywhere in london then go back home as you have just enough battery for a work-home journey.
I need to increase my battery capacity because I don't have enough battery to go out to meet my friends after work... without being out of battery. So even if I only use around 350-400Wh daily, I need the double for cases where I go out with my friends or any other occasion.
Now, let say you want to stick with your 300wh lipo. In HK europe, the lipo cost around 0.5-0.6$/wh. So a 300wh lipo would cost 200-250$ shipping cost included.
Now, let say you want a bigger pack, something like an A123 36V20AH (720wh). It would probably be around 450$. But you'll have 2.5 times the lipo capacity, you won't have any charge hassle with the balancing to care about, and you'll be able to sell it at half price in 2 years when we'll have better battery. So in total the battery would be half price.
And of course, you can push the motor to 1000W continuous without having to worry about the range or diminishing the cycle life of the battery.
That's my little crazy calculation. The price is so low for A123 that I'd like to try them