Sharon, the travel agent probably didn't trust that you would grasp the importance or had the full knowledge for providing the EXACT names of the granddaughters. Imagine the dread when the passports arrive and a name doesn't match, rendering the ticket worthless? That's an expensive mistake, which ultimately isn't the TA's fault, but would likely be made to be.
Back to the OP. Have you tried Airbnb for an apartment for your dates? Two of our longer stays in London were in apartments, the latest in December.
I got a good deal at the President Hotel on Russel Square one time and at the National across the way another time. Not my favorite hotels, with crappy breakfasts buffets, but they had promo rates under 100£ and I like the area.
Try Agoda.com, as well as Booking.com.