If we had better planning for our daily routine, where we always know that prayer time is what everything else rotates around, then we will always have prayer time prioritised. This will mean that when it is prayer time, whatever is necessary to have for prayer would have already been thought through.
It's always best not to delay your prayer, and in cases where you cannot at all find a corner or a room, or a place indoors or outdoors to pray in some peace, then you will need to see how much you are able to keep focus and concentrate.
It will not be haram for you to delay your prayer a bit, as long as it is within the time frame for that prayer. At the same time, if this situation is regular, and you are frequently in a crowded place at prayer time, you should find alternatives, so that you are able to pray on time, which is the best and most recommended thing to do.
And Allah knows best.