Your partner/ child's father or mother is more than welcome, Regarding COVID pandemic as your the same household (if your households are different please let us know) this is still the case. But least possible human traffic in the clinic is preferable.
Please note multiple people in the room can increase a stress event in kids, particularly when brothers and sisters are crammed into a treatment room and focusing on the child's reaction.
The Wimbledon clinic is more sparse than usual, so they could wait outside the room with a door open, in reception or in-room - it's really up to you how your child is best calmed.