London hotel/apartment wanted - summer 2017

This company has a 3 bedroom you could use: http://www.castletownhouse.co.uk/3-bedroom-vacation-apartments-london.html.

It looks like it's 330 pounds per night for next July. Three bedrooms and one of the baths is ensuite but not the other. We stayed in one of their 2 bedrooms a few years ago and it worked out nicely.

Yes, I’ve noticed that air conditioning has limited my options. Unfortunately, for my mom has some breathing issues so it’s required.

Sorry I don’t have the verbiage down just yet. I mean to say no shared bathroom — as in a private bathroom that only we can use. That can be in the flat, and we can all certainly share a single bathroom.

If aircon is a must, you may need to go the route of a serviced apartment. I've used a company called Go Native a few times - they have a lovely block of apartments near Monument, a fascinating area in the financial district (The City) with easy access to most sights via foot, bus or tube. Not sure if the prices or size will work for you, but I've rented a one-bed and a studio at various times and couldn't fault them. They have other properties too.

http://www.gonative.com

Since £400 a night is within your range, I will mention this beautiful 2-bedroom, 2-bath apartment we rented for our family (6 of us) last May:

https://www.tripadvisor.com/VacationRentalReview-g186338-d8363557-Gorgeous_Waterside_Apartment_near_Tower_Bridge-London_England.html

It is nearly brand new and with hardwood floors and leather sofa, very allergen-free. You could send a message to the owner (Kim) and ask about the air quality situation. We just opened the doors to the deck to admit fresh breeze off the river when we wanted, and never touched the heating/cooling.

The location is excellent for walking but also convenient to the bus ( RV1). Tube is an 8-minute walk.