Name the fruit

At first thought they were blackberries but they aren’t black. But don’t look like raspberries either??

Loganberries?

or Tayberries

 

I was going to say it's most likely one of those two!

 
Loganberries are purple-ish and Tayberries are deep red, on my plot.

Of course the other option is a Boysenberry but they often have the bristles on the berries like a wild blackberry and share the wild blackberry taste, don't think this plant is one.

I think like the other berries, you can get thorny and thornless plants.

I know what you mean about Tayberries - I thought I'd dug all the thorny ones out - but they're still trying to make a come-back  and overgrow the thornless one I planted 

(why does spellcheck object to 'thornless' FHS!)