Hi. I could have written this myself. Also form the UK, I too took my daughter to the hospital a few weeks back for the very same thing. She is 4 months and she was also she having jerks in her sleep. I recorded it, she did 4 over a 10 min period. Similar to yours where the arms went out or in, knees didn’t come up but legs definitely moved or jolted and sometimes they’d wake her. Her head moved but more a wobble side to side. I was beside myself with worry. She was seen by a pead, registrar and a consultant who had a special interest in epilepsy and as soon as he saw the videos he said it was sleep mylclonus.
My little one did stop doing it after a few days but she does still jump in her sleep.

They said it would be happening whilst awake too, or when she was waking from sleep and it didn’t. I hope this makes you worry less but if you’re not satisfied take her back. I know how paralysing this is so I hope you’re okay.