One of the benefits of lockdowns 1 and 2, for me, has been that our usual dog walking park is no longer isolated. I understand your feelings compleletely.
I don't think you were being overly anxious. I think you had your own hackles up and there's a reason we respond instinctively to certain situations. Your situation would unnerve me as well.
I think, in all of the years of walking my dog, the one time my gut transformed itself into a pit of doom and fear was once in Gunnersbury Park. I just found myself totally isolated in an area where all I could do was keep walking forward until I found a gate to exit. At that time, most of the entrances/exits were temporarily gated off so I couldn't just walk out of the park. I had to keep walking until I got to an open exit. It was unnerving.
Another time, about 5 years ago, I was walking along the towpath in West London. I was entirely alone, feeling a bit nervous about it (I was walking towards a footbridge that I needed to cross). About 15 minutes after I'd walked past the boathouse, just before crossing the footbridge, a woman had been mugged and stabbed (not fatally). I'd seen the two guys ealier along the footpath and they looked a bit unsavoury, but I didn't give it much thought. I was very surprised when I later returned to find the towpath cordoned off with police everywhere.
I've been held at knifepoint by a man (not in this country) and my son, two years ago, was mugged at knifepoint by a gang in a local West London park. Once, on a dog walk, about 3 years ago, I was on a very remote meadow with one other dog walker (a man), who got talking to me. He then put his arms around me and squeezed me tightly mumbling random shit. It scared the hell out of me. I was very scared and shocked by how fast our conversation went from dogs to where we both come from originally, to being hugged and held and whispered to against my will. I was terrified.
So here I am with my 'bad' stories, not intended to scare you or anyone, OP. But always trust your gut. At the same time, murders in London parks are uncommon and infrequent, which is reassuring.
But I do try and stick to populated dog walking areas ever since that 'creepy hug' I got. I'd do the same, if I were you. You want your dog walks to be peaceful and therapeutic. 