Actually after having a closer look it appears you have raspberry at the front and bramble at the back of a clump.
I agree some of the leaves at the front look more raspberry than bramble. It's hard to tell without seeing the stem/how it's growing as younger blackberry leaves can look a bit raspberryish 'til they're mature and have all the serrations on the side. On balance wild raspberries are rare compared to blackberries so I'd be on the side of treating the whole patch as bramble.
Personally I'd nuke the twat from orbit before it settles in and you have odd bramble patches springing up everywhere in a year or so. I get them here popping up through the underlay on the little pebble section I have and through the stone walls etc., as well as every fucking where else. Once it gets in it's a bastard to get rid of, the spiky owchy git always has a few underground runners you'll miss that will pop up fecking miles away from the original plant. And it's a strong bugger- you won't just pull it out, it will fight back. And win, in my experience unless you have a very sharp spade, and lots of patience to track down each runner.
That said though I have no shortage of wild blackberries on the doorstep, so it's not something I feel a need to grow in the garden. They grow everywhere and if they're in your garden you'll have a good patch nearby most like, but depends if it's in an area you'd want to pick from (by a road etc., would put me right off).
Don't fall into the trap of letting it stay because you think the berries will be great and you'll eat them/use them all and be a living a Gwyneth Paltrow like existence of yoga and organic berries and magic pebbles for nowt. Done that now three years in a row with the raspberry canes that have gotten out of control (minus desire for magic rocks). There's only so much jam etc., that you can make, and you only get the benefit of them fresh for a few weeks unless you have a huge freezer. And blackberries aren't half as tasty as raspberries or blaeberries etc.,
I'd still nuke the twat from orbit and pop in a few raspberry canes instead though. If you want berries that is.