OK I got my new router today, and so far no reboots.
I got a Linksys WRT54GS.
http://bbc.co.uk/weather works fine.
Also the speed is much nicer.
Downstream 9309 Kbps (1,163.6 KB/sec) 10053 Kbps (inc. overheads) Upstream 492 Kbps (61.5 KB/sec) 531 Kbps (inc. overheads)