Can I get Lip filler on strawberry birthmark? Left as a small scar on my lower lip (Photo)

I have a strawberry birth mark on my lip however it’s only a scar that has deepened a bit now so the small area of the mark is deeper then the rest of my bottom lip. Will I still be able to get a lip filler done. If so which place can I go to in London. I’ve had it for years it was worst however it’s only left a mark/ scar now. I had laser done it when I was young. And I’m only 19 now. It’s a big insecurity that I have and I’m hoping there will be a solution. Thank you.