I'm sure that hotel has been mentioned on the forum; try the Search function. I vaguely remember generally-positive comments, so the information I'm posting below should not be interpreted as an effort to discourage you from staying at the Cherry Court. I like to support independent hotels.
As I recall, the Cherry Court isn't air conditioned, so I'd recommend checking the actual, historical, day-by-day weather data on timeanddate.com on your travel dates for the last five years to see what the risk is of hot weather. For me, the early-September 2021 data looks risky.
The hotels around Waterloo Station are convenient to both the Waterloo and Westminster tube stations. I've stayed at the Premier Inn County Hall, but there's a Hub by Premier Inn in that area as well. The Hubs, less expensive (but normally more costly than the Cherry Court) have small rooms, but as a solo traveler you might be OK with that; I would be. Do check to see what the website says about whether you'd have a window if that matters to you.
Premier Inns are efficiently-run and well-priced. They are not charming, but most are air conditioned. Premier Inn rates are usually quite a bit lower for early reservations. There are both refundable and non-refundable options; the gap between those categories is likely to widen as the arrival date approaches. The "Flex" option allows cancellation up to 1 PM on day of arrival. The "Advance" option allows cancellation up to 28 days prior to arrival, after which the entire cost of the reservation is non-refundable. However, as I read the cancellation policy, it appears you can shift the dates of a reservation for the same type of room at the same hotel and just pay any difference between the current and original rates.
The Cherry Court website indicates a 7-day cut-off for refunds, which would make me nervous, especially for the first hotel of a trip. The longer you're staying, the greater the risk when a hotel is going to hold on to your entire payment rather than just the cost of the first night.