This is what we did: When DS was able to sit up in a highchair (we had the tommee tippee healthy care booster seat which was a great size for a small 5 month old and grew with him) we let him sit up at the table with us when we ate.
Once he started showing interest in the food, (which wasn't long!), we let him have some bits to explore and gum on. This is perfectly safe as long as they can sit up straight with support, and they are picking it up themselves rather than you holding it to their mouth. If they gag, that's fine, because they are just working out how to move the food around their mouths. If they are sitting up then a gag will just result in the food being spat out (lovely!) though of course you should never leave your baby alone to eat.
After a while of gumming on things, generally dropping it, not eating massive amounts, but being happier in general, then he seemed to "get it" suddenly and ate a lot more. I would definitely do it this way again. You need no special equipment and you get to eat a hot meal at the same time! Plus you know that your baby is definitely ready as their development is showing you they are capable. I believe the NHS recommends "the banana test" now as well, which is the same thing - you put a chunk of banana in front of them and if they can grab it, put it in their mouth and swallow some all by themselves, then they are ready to wean. It's quite amazing actually watching a tiny baby feed themselves :)
HV is talking rubbish though, I agree. A friend of mine was giving her DS two cartons of hungry baby milk at every feed and he was still hungry, but she managed to hold off until 5 months. It's perfectly fine to give them more milk if they need it, and milk is so much better for them at 4 months than food - food should only really be little tastes to begin with anyway. You could try different formula brands perhaps to see if one is more filling?