Heathrow is my favorite place in Europe to shop LV. I arrive early so I can shop both terminals. Stock is always amazing and they have the best prices. Be aware, when you shop between terminals you will have to go through full security screening on the way into the other terminal and on the way back to your departure terminal so arrive very early. The personal shoppers will escort you between terminals.
Once in the states, declare everything! Sometimes you will get a nice customs agent who will let you go with no tax charges. To date, I have always declared my goods and every time they waived me through without taxing me.
Even if you are charged it's only 3% if you have items valued from $801 to $1200. After that, the tax varies on whether your goods are leather or not.
If you are traveling with your husband or partner, sister, brother, etc you can combine your limits so you are able to have $1600 worth of goods without paying customs tax. If you are traveling with multiple family and wife or husband or boyfriend, girlfriend etc you can all file together. A family of four can have a limit of $3200 without tax.
Safe travels and happy shopping!