In reply to mike123:
The main types of bmx are street/park/freestyle or race. If your sprog is wanting to do tricks then a cheaper, robust crmo frame might be best, but for pump track or race use, then a lighter and longer geometry race frame (eg aluminium) might be worth it. Beyond that, you get what you pay for, with lighter, stiffer components for more money eg carbon forks, better wheels etc.
Redline and Haro are big names that specialise in race bikes. I'd go for 2nd hand, and get a complete bike that is the right size now, rather than getting one that is big and unwieldy "to grow into". You should be able to pick up a decent 2nd hand race bike in a small size (they do 16" and 18" wheels with correspondingly smaller frames as well as the standard 20" wheels) for £200, and you could prob sell it on for not much less if junior loses interest. A 21.5" top tube frame is typical for an average adult rider.
Useful uk race bmx forum, with for sale page:
http://forums.bmxtalk.com/viewforum.php?f=3
pinkbike, for more bmx for sale ads:
http://www.pinkbike.com/buysell/list/?category=23&location=193-*-*
Winstanleys, for typical range of bikes (both street and race):
http://www.winstanleysbmx.com/