It depends on how go with the flow you, your husband, and the other couple is, and what you plan to do in London. If you have been to London dozen of times and are imagining that the 4 of you plus baby will be renting an apartment and hanging out with occasional touring and occasional dinners out, it may be OK.
I have traveled with babies. It was not easy but it was doable. Would I have chosen to do so? No, honestly I would not have done so. There are always people who have angel babies and there are always parents who will say "no problems" but if your friends haven't been parents before I don't think they have any idea what it is to be a parent of a 4 month old at home, never mind on vacation.
You are in a lovely restaurant and.....the baby is not happy. You don't know why. Or you do know why....but you can't make the baby happy. You will not be happy that the luscious (and expensive) dinner you just ordered is not going to be able to be eaten hot. The neighboring tables may smile and coo, but if that baby doesn't settle down quietly and quickly no one is going to enjoy their meal. One of you will be walking outside with the baby until the baby settles down. Even if it is drizzling outside. Those staying in the restaurant (the other 3 adults) will not quite be able to enjoy the dinner bec everyone will be thinking about the person walking the baby. Ditto any museum, point of interest, boat ride, movie, theater, church tour, bike ride, etc. When the baby is good (ie asleep and or quiet), it will be easy as long as there is a stroller/car seat/snuggly available. If the baby has those moments which most babies (and people) do, it is usually loud, it can be scary, and messy. It can be worrying and frustrating. Babies can be silent, wondrous beings...but they also pick up viruses, get ear aches, and can be awake when they should be sleeping. I don't mean to sound hard hearted---babies are terrific. If you 4 adults can be flexible and don't mind tailoring your activities to the baby's current mood, go for it. If you feel like you might feel trapped or resentful when you walk into the museum or concert etc and you have to make a quick exit, I say rethink the timing and perhaps try again later....3 year olds are much easier. :)
Either way, have a wonderful trip to Germany!