The B4 is a better car than the X-Pro, but if you get your daughter the Madrat, there is a good case for the X-Pro in that they are basically the same car, so you can share spares etc. Got to make life easier doing that.
Ezruns are mainly from Hong Kong. You can get them here, but expect to pay a lot extra for doing so as you are just paying for someone else to import them.
Giant Cod sell the speed controller but not the motors, though you can use other motors. Nothing more than a 7.5t though.
You can get cheaper chargers than the Core, though I'd avoid anything that charges at less than 5A.
You can go brushed for now, since a
brushed esc costs as little as £24. Please note you'll need two as the Madrat comes with a motor, but no esc.
Brushed motors with decent performance can be had for £24 too - the B4/X-pro will need one but your daughter will be fine with the Madrats stock one.
Edit - Actually I'd get the following:
Madrat brushed RTR for daughter.
X-Pro for yourself - build with her. Its virtually identical to her car so the experience is the same.
Radio for the X-Pro
Ezrun .8.5t system for X-Pro
Lipos off hobbyking
Imax charger from the same place
Should be doable inside the budget.