They don't know electricity usage by house unless OP has a smart meter. Which is why electric bills are often so far out!
The power to the house won't be a problem. Houses have at least a 60A incomer, usually nearer 100A.
20 of R9 280X at 250W TDP = 5000W
4 of R9 290 at 275W TDP = 1100W
So 1000W per 280X system, 1100W on the 290 system.
Allowing for losses in the PSU (antec don't publish an efficiency curve) we'll go with 85% at that power level.
1000W/0.85=1175W
1100W/0.85=1295W
So input power is 1175*5=5875 + 1295 = 7170W total input.
7170W/240V = 29.875A
Given that most domestic sparks will install sockets on a 32A ring, you'll be OK. Just. Chances are if you tweak and underclock then it will run a bit lower. As long as the install is good, and you space the rigs around the ring (no more than one per socket, if you have 6 double sockets going in, put one on each socket.
Just don't switch them all on at once. The inrush probably will trip the breaker!!
Just a thought. Do check your incoming supply. Bear in mind that things like electric showers and Domestic ovens can pull up to 40A, you might want to consider what might happen if you run your rig whilst cooking dinner in the oven and go for a shower. Blowing main incomer fuses is something that can only be rectified by the power board!