Is lamb a regular dish or more of a Christmas and special occasion dish? I’m not in the UK so I genuinely don’t know. Not sure that you can get lamb at a fast food joint like you can with beef burgers.
I’m in the US and can get lamb at fast food joints. Go to any Mediterranean shop for a gyro. Afaik it’s even more available in the UK since it’s primarily sold as people food, not dog food like the US market.