"in London.... 5pm...." Is that at Heathrow at 5pm or in Central London at 5pm? Three and other shops may be closed (please check) by the time you get into London.
As many have said - wifi is free around many places in London - notably coffee shops and perhaps where you're staying?
If you need to call someone the night before back to the USA and you have access to wifi - Google Hangouts offers free calls to all USA numbers.
During the day when you're out and about - use "Dial-a Code" (I will link it below): it lets you save on PAYG rates to international numbers. It's 3p per min, equivalent to the UK rate (Three's 3-2-1 PAYG Sim).
In terms of coverage, Three provides a consistent 4G service across much of Central London. I experience only 2-3 bars usually but it works very well for me.