I am not sure you have much spare time !
As you probably know the V&A and History museum (along with science museum) are very close to each other so you could spend a day there.
If you like Museums then the British Museum is an amazing place, but maybe you will have had your fill of museums after the V&A.
London is a GREAT city for strolling round. In almost every area there is something of interest to see. The area round Parliament, Westminster Abbey, Downing Street, Trafalger Square is full on interest and you can easily spend more than half a day walking round there.
The Tate Modern in the south of the river (next to wobbly bridge) is interesting, and is next to the rebuilt Globe Theatre.
Then there is St Pauls, Tower of London, London Bridge, Bond Street, Leicester Square, Buckingham Palace, St James Park, Harrods, Regent St, Fortnum and Mason, National Gallery and so on.
There are also the lovely Wren churches, and some quiet small squares surrounded by historic houses.