At what age does the board think children are responsible enough to be left alone in the house?

I'm talking here about 1/2 an hour to an hour in a controlled manner, rather than being dumped in the house to fend for themselves for the day.

I have two boys 10 (nearly 11) and 9 (nearish 10). I left them for 1/2 an hour to start the process of developing some independence in them. The door was locked but they had a well defined escape route in the event of an emergency (the downstairs window which they use anyway when they are messing about). The eldest had his phone which he called me on to let me know everything was okay. Both were very comfortable with being left and they are both bright, sensible boys.

I'm conscious that when I was their age, I walked nearly a mile to school and back, crossing two main roads in the process, without the presence of an adult. I also played out with my mates for hours at a time often wandering a mile or so from my house.

Unfortunately I've now been contacted by my ex wife, quoting the Children & Young Persons Act and threatening me with her solicitor.