A couple weeks ago, we landed at London Gatwick Airport (not Heathrow), but there was similar situation - buying our tickets for the next departing Victoria Express train from Gatwick, we also bought our Oyster Travel Cards from a helpful, live person. One trick with the Oyster card, you scan it to get into the Underground, and again when exiting. Once, although my card opened the exit gates, the transaction somehow didn't register in the system, so it turns out I was charged the highest possible fare for that trip, rather than the normal rate for the 4-stop journey I actually took. On the next-to-last day in Lodon, I should have had plenty of pounds left on my card and the system wouldn't let me through the In gate, saying I only had 40 pence left on the card! An attendant checked the records and restored money onto my card, and said sometimes if you go thru the gate too fast, the system doesn't credit you for scanning yourself out. Take an extra 2 seconds and ensure you've accurately scanned your card and are credited fairly for your Tube trips!
Also, donation boxes are at the entrances to museums, and museum maps for the National Gallery, Tate Britain, etc. are priced at 1 pound apiece, but are kind-of on the honor system, with a box near the map racks throughout the museum where you can drop in a pound or five, so that's another place where you can drop in a donation.