Which Apple (or other fruit) is this?

[ameno]

As others have said, it's definitely a Japanese quince.
The main way to distinguish it is that it will still be in leaf this time of year. Japanese quince are semi-evergreen, and only loose there leaves after a really hard frost, whereas any other tree or shrub which bears similar looking fruit are fully deciduous.

The leaves are spot on compared to my plant.
Mine flowered but did not set fruit last spring. I am hoping for fruit this year.

Is it a single-flowered variety? If it's a double then it will set few, if any, fruit, as they extra petals are modified from the anthers, and thus double flowers have no pollen.
I have a beautiful peach coloured double in my back garden, and it has maybe two or three fruits a year at most, despite being a large bush with hundreds of flowers each year.

[gardengnome]

It does provide a fair amount of fruit, but most of the leaves and all of the fruit has dropped now.
I pruned it this afternoon, as it was spreading out away from the border where it’s planted and causing the lawn to die.
From what I read, it may not fruit this summer now, but it had to be done.

Out of interest, would fruit I pick up off the ground now, still be okay to make liqueur?
I have some experience making sloe gin.

[Nicos]

In Normandy, the cider apples are left to rot on the ground until between November and now before being processed into organic farm cider. Adds to the flavour apparently!
No harm in trying!

[ameno]

It does provide a fair amount of fruit, but most of the leaves and all of the fruit has dropped now.
I pruned it this afternoon, as it was spreading out away from the border where it’s planted and causing the lawn to die.
From what I read, it may not fruit this summer now, but it had to be done.

Out of interest, would fruit I pick up off the ground now, still be okay to make liqueur?
I have some experience making sloe gin.

As long as the fruit is still firm, then picking it up would be fine. Just cut out any bad bits. I collected some fallen apples from the communal orchard at my allotment last January, and they were absolutely fine.

As for pruning, most of the flowers are produced on the bottom-most 10% or so of the previous year's growth, so it's best to just shorten by 90% or so.
I actually prune mine in March or so, just before it comes into flower, as the flower buds are large and obvious by that point, so I can cut growth back to the flowers and no further, meaning that I don't accidentally remove flowering wood and it means the flowers are more exposed and thus more on display.

[burnie]

I would suggest that any sugar left in the fruit will be useless for making alcohol this late in the year, cider is usually made in late summer early autumn before the sugar turns to starch. I did try making Quince wine back in the 1980's, it wasn't very nice to my taste, it got mixed with some rhubarb wine which sweetened it up a bit.