British 00 Scale

My daughter gave me a model train set today she purchased in Wales. It is made by Hornby. They say in the set it is 00 scale.

The track appears to match up perfectly with track from my old HO scale set. One of the Hornby cars runs well on the HO track with no wobble, slop or binding.

Is the British 00 scale the same as our USA HO scale?

Not quite the same. I model US and european HO (1:87) and British OO (1:76 I believe). OO is a bit of a compromise it uses HO track but the actual equipment is a little larger scale wise. I understand the reason for this was dates back to the start of HO/OO. Generally the motors available for model trains were to big for British HO scale models so manufacturers scaled up the bodies of the engines. Now this is no longer an issue but OO has a large and loyal following and so it is not likely to go away any time soon. There are some British HO models out there but not many. I have several Hornby models and they are okay. Until recently though I have found them to be rather toy like when compared with British Bachman or the now defunct Lima. Hornby is going through some significant cahnges and their mouth watering class 50 diesel is made in the same Chinese factory as P2k from what I have read. I love British rail and would encourage you to research the railways of the British Isles further. I will quite happy running a British Railways Inter city 125 HST along side my Amtrak Acela.

Not exactly. When HO scale first started prior to WWII manufacturers of British models had a problem fitting motors into the models since British locomotives are smaller than American locomotives. To compensate they changed the scale from 3.5 mm to the foot to 4 mm to the foot. But they kept the track gauge the same. So British OO is 4 mm to the foot, but runs on HO gauge track. American OO corrected the track gauge, but American OO is dying out. British OO is very strong.
Enjoy
Paul