Simple past being used more in BrE

I'm a native British English speaker and I was wondering the other day whether, as a result of the influence of AmE, I am now more likely to use the simple past in instances where say 20 years ago I would use the perfect.

For example if I was leaving the house with some one I might say either 'Did you turn the heating off?' or 'Have you turned the heating off?'. However I wonder if the former would have sounded off when I was younger, as in standard BrE it is usual to use the perfect to refer to an action in the past that is relevant to the present moment. Has my brain has undergone a gradual shift as a result of listening to American TV and films, so that I do not realise that there has been a subtle change in the way I speak, or have both tenses always been standard BrE? I really can't be sure.

'Did you turn the heating off?' - We are about to leave the house, or indeed have already shut the door behind us.

'Have you turned the heating off?' - At most, we are approaching the door, and turning the heating off will therefore be easier than if we were outside and needing to let ourselves back in to do so.

But those differences are only suggested by the forms - I doubt they are absolute usages. And I'm not sure that that sort of difference isn't found in American usage still (I'm British).

Too idiosyncratic to define any concrete rules...

I would like to find out more about this too. Is there really a difference in the way the past tenses are used nowadays in the UK? To be really sure we are only considering recent usage maybe we should only consider how young people speak.

I just ate an apple. Not hungry anymore.
Did you see my keys? I can't find them.
I already checked the lights. We can leave.