Ok so just back from our 20 week scan. Baby all well which is the main thing. Husband came with me and got all the way to the waiting room and it was only then he was turned away. We didn't receive an advanced notice call from the maternity team/sonographers. I'm based in North London if that helps (Chase Farm Hospital).
When I got in there I asked if I could FaceTime him or video and they said no as it is a diagnostic test. That was when I had a little cry (gonna blame pregnancy hormones). I think she felt sorry for me so towards the end she asked the nurse in there who was taking measurements to pass me my phone so I could take pictures.
So if and when they let you do this, do a quick switch to video! I got a couple of clips 5-10 seconds long which he was pleased about (and of course we wouldn't have got that to keep under the normal circumstances). I'm not sure that they are printing photos for expectant mums at the moment so just be prepared for that and make sure your battery is fully charged!
Finally this scan really is as they say, diagnostic. There wasn't much in the way of things to see, other than the couple of snaps they let me take at the end. So I don't think my hubby really missed out on all that much. Plus, like you say, we can get a private scan done at a later date when hopefully things are more relaxed. Will be cool to get a 4d one done too.
Anyway, we decided to find out the sex given all the doom and gloom at the moment and we are having a girl - absolutely delighted and will give us some planning now for decorating the nursery, buy clothes and choosing a name.
Also, my friend is due at the end of May and I believe you are still allowed a birthing partner under the current circumstances m, but just the one.
Hope this helps!