I really wouldn't go before 8 weeks.
I was desperate for an early scan... In the end, I booked one for 8 weeks, but started bleeding in the 5th week and had a scan at exactly 6 weeks in the EPU. They couldn't see much... the gestational sac and the yolk sac were clear, but there was no heartbeat yet, and that meant they can't confirm a viable pregnancy. The sonographer saying those words stayed in my head for WEEKS.
The EPU booked another scan for two weeks later, which is the earliest that they'll do one, as a week isn't considered long enough to see much growth... and private places don't like to scan you again within 14 days either. The two weeks feels like forever, and it's made my anxiety so much worse than it was. I didn't even necessarily want to see the heartbeat...
It's not just me... there's loads of us, on here and elsewhere, that find them to do more harm than good before it's too early to see that the baby is still okay. My scan was last Monday, there's a good few people since then that haven't been able to see the yolk sac either, or get left with a "pregnancy of unknown location" because it's so early.
Babies are hard to measure before 12 weeks, they grow randomly and can be showing as 5 days bigger or smaller at any point, which is why the NHS doesn't date until 12 weeks, so even if you know exactly when you implanted, it doesn't mean you know how big the baby will be that early...
And the age-old problem remains, that they only tell you that the baby is okay in that snapshot, and then the reassurance can fuel more anxiety... and lead to you having loads of scans.
I can't say I wouldn't have an early scan ever again, but I'd wait until I was 8/9/10 weeks. It feels like forever, but honestly, the waiting and worrying is nothing compared to the waiting and worrying if they can't see what they want to see because you're too early.