You are in for a special time, do not let the weather bother you, it will be better than most places. Likewise, the city does not shut down. There are holidays but you will be just fine.
You should start out and look at previous "insider" tips and experiences on London in this site. Likewise, you will need to decide where to stay. You should try to get in Central London and depending on how many of you are traveling you should be able to do this reasonably.
Good luck, and again, review pictures and previous experiences on line here.
It's probably too late and you already know, but London assuredly does not shut down in July and August. Europeans do typically take their vacations in the month of August (though that is starting to change at least in length).
If there is one drawback to going anywhere in Europe in August it is either weather (not a problem in London, but elsewhere) or being surrounded by tourists, many of whom are Americans. It doesn't quite give you the same feel as if you went in December or January when fewer people visit.
But by no means do things close down. European economies are geared to tourism, so you'll be able to do anything in London in August that you could do during the rest of the year.
Have fun, if you haven't already!
An advantage of visiting during this time frame is that the Queen goes off to Scotland near the end of July and through August. That means that Buckingham Palace is open for tours. It is not open to the public the rest of the year when the Queen is in town.
Definitely worth taking the time to tour. Buy your tickets in advance at your hotel or on line, and avoid super long lines to get in. But get there before the first group is scheduled to get in -- as the line for those with tickets in advance also gets long quickly.
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