You could just knock on the door and ask! Most gardeners are happy if anyone takes an interest and admires their roses.
I remember my mother asking me to knock on the door of a house on my way home from junior school to ask the name of a plant she'd seen growing in one of the front gardens. I did as i was asked and went home with a bag of cuttings for my mother. Not sure you could ask a small child to do that these days!
It can be really frustrating trying to find the exact same one, especially as the colour and growth of the same rose can vary slightly according to location, growing conditions and even the time of year. I like Flower Carpet Amber as a possibility, but also look at Amber Sun and Mrs Oakley Fisher.
Things to look out for in your hunt are flower colour and form (single, semi-double), height of the bush, whether it is fragrant and what it smelt of, shape, glossiness and colour of the leaves, colour of the stems and if new growth is green or starts off reddish. For example, Mrs O has the closest in single flower form and colour but dark coloured stems. Amber Sun looks to have a similar colour and the dark, glossy foliage looks right, but, like Flower Carpet Amber, the flowers look a little fuller.
Good luck with the sleuthing!