I'm not sure what to suggest here - my HV's (I'm UK too!) have always said that you need to let them feed until they stop by themselves, if they are draining bottles you need to add another oz. I've never been told to limit feeds and the only reason to would be if he was taking big feeds and vomiting them back up again.
If he was breastfeeding that's exactly what he would do - feed until he is full and stop - and you wouldn't know how much he had taken. 120ml is only 3oz, my DD was taking that much in her first week or so and then steadily increased so she was taking about 6oz (240ml) by the time she was 8/9 weeks old.
It is likely that he would fall asleep if he was hungry - he'd had some food and may not have been quite full but full enough to fall asleep because he was tired. I wouldn't want to get into the habit of rocking to sleep - it's a hard prop to break, also if you are trying EASY he needs a bit of activity time (nappy change in your case!) before he goes to sleep not to go straight to sleep after a feed.
It's up to you - I've learnt from experience that all HV's will tell you something different so I nod politely and do what I think is right
. I would be offering bigger bottles for a day or so and see how he copes with them, if he is keeping them down and is settled then that's what he needs. If he is vomiting back feeds then I would limit them to 160ml for now but he may then need feeding more frequently than 3 hourly.
I know he was a bit prem - has he had a clean bill of health since then? What week was he born - was he 36+ or 33+? If he was 36+ he was very close to full term so it's not such a consideration than if he was 33+. My good friend had both of her babies a few days shy of 37 weeks and neither had health problems or were considered prem.
What do you think?
Laura