Missed miscarriage...surgery?

Polly
I am 8 weeks 2 days pregnant but it seems the baby stopped developing at 6 weeks, no heartbeat on the scan. These are private scans that I have paid for, not NHS (UK free system). 
I had red blood on Thursday whilst at work, came home and the doctor came to see me, didn't examine me but said yes if no heartbeat then likely this is your bodies way of clearing everything naturally, after she left the blood stopped and I've had a tiny bit of brown discharge. Had another private scan last night and they confirmed this is a missed miscarriage. Have a private appt on Wednesday morning for consultation. Just wondering your thoughts on whether to have D&C or to wait and let nature take its course but I understand this could take weeks. Really don't know what to do for the best. Either way is awful but I feel like I need to grieve and move on rather than grieve for weeks and weeks and have a lot of cramps and discomfort in the process? Thank you for reading and sorry for this lengthy post!