What router would suite a house like mine?

In my house (I share with 6 others), we have a total of 21 devices sometimes simultaneously using the wi-fi access from our BT Home Hub 2.
That's 7 laptops, 3 Xbox 360's, 5 Ipods, 2 Iphones, 1 Nexus, 1 3DS, 1 WII you and 1 TV.
As you can imagine it gets very laggy, but this has nothing to do with the provider or contract but the router itself.
As well as this, the biggest problem is the wi-fi drop out, which frequently occurs when the router essentially stops all wi-fi, and requires a reboot to work again because of the 12 or so connections using the wi-fi.
We're looking for something (ie. Router, access point etc.) that will help solve both the drop out problem caused by the amount of devices using the router, and the lag sometimes caused during online gaming.

Any advice?

I would suggest the Cisco Linksys EA6500 but I don't think this will solve your signal/wi-fi drop out.
Considering the amount of devices you have, there's NO router out there that will suite you needs unless you separate your gaming devices from the rest.

It's all about the signal bandwidth. A single router will always equally allocate the signal bandwidth among the devices connected to it, unless you program the router otherwise which is rather cumbersome to most users. For experts, they can do this and allot only a small amount of bandwidth to cell phones, tv and laptops. But then again, if all of them streams videos, then that's where the problem would start.

You have to have at the VERY LEAST 3 separate routers or Wi-Fi access points to satisfy your signal needs. 1 for the gaming consoles, 1 for the laptops and 1 for cell phones and TV.