As a GM who was in your exact situation (except I had closer to 9 players at the table) I speak from experience when I say:
Rooms can get cramped.
It is probably a good idea to add a few five feet to either side of a room. Leave hallways and doors alone, though, those are excellent ways to funnel your players so that their numbers aren't very overwhelming.
A few times I have increased the room size is: WARNING! SPOILERS!
1. The fight with the Green Dragon in the Ruins of Thundertree
2. Various small rooms within Wave Echo Cave
3. Any room where a random encounter occurs
This is, of course, optional but I found that this lessens the frustrations a bit when several players are trying to attack one bugbear. If you like making an encounter feel cramped, feel free to ignore this.
Players will swarm your creatures
It's not often creatures get into a situation where they are fighting with inferior numbers. Cowardly races such as Goblins, which are featured more in the LMOP module might not take on 7 PCs if they number only 4.
You will have to increase the number of Goblins or introduce some other creatures into the mix to give the goblins a fighting chance. To get this right, you will have to study the encounter difficulty based on the budgeted experience for each encounter as intended (i.e. if there are only 4 players) then workback the intended difficulty using 7 players. See wax eagle's answer on budgeted XP for HOTDQ (another module), he explains it better.
Boss monsters will be a breeze
As a workaround to this, you can adjust their Challenge Ratings as you see fit, still basing on the intended encounter difficulty. See my answer on scaling down a creature's CR. Though it is for scaling down CRs, it is still applicable for scaling up.
One Mini-boss monster I especially created was:
King Grol, the leader of the Cragmaw Goblins and 2nd-level Barbarian.
I gave him resistance to BPS damage, a +2 to damage rolls and Reckless Attack. All of these features can be fine tuned to the rules in creating/modifying creatures.