The place I stayed very recently and also in September 2017 might work: Vincent House, 5 Pembridge Square, Notting Hill. Booking.com shows availability every night except September 13, and if you contact the residence itself through its website (which will probably save you some money, based on my experience), they may actually have room for all the nights you need.
The website says the rate is £95 for stays of less than five weeks, but I've been paying less than that. I think the website quote includes dinner as well as breakfast. For this year's stay of 12 nights I paid £80 per night with breakfast and without dinner. I believe paying for breakfast is unavoidable, but it's better than average. It's buffet-style with all the components of an English breakfast (eggs undercooked if it's a day for scrambled, and no crisp bacon, but there are always hard-boiled eggs, plus frequently something I'd call ham). They always offer fresh fruit (melon and pineapple recently), several kinds of cheese and meats (hot and cold), sliced tomatoes (in season) and cucumber, yogurt, and cold cereal. Sometimes there's something special like ricotta-filled crepes or bagels with cream cheese and salmon. A negative is the weekday breakfast schedule of 7 AM - 9 AM, but if you walk in at 9 AM (usually even at 9:05), you'll find most of the food still accessible. Weekend hours are a bit later.
The location is one longish block from the Notting Hill Gate tube station, which gives you immediate access to the Central, Circle and District lines. It looks like a dormitory on the outside, but all the other buildings on the street are attractive 4-story (apartment?) buildings that look like large row houses. It's a very convenient walk to the Portobello Road market, but the location of the residence is quiet. Near the tube station are two supermarkets, Boots, two ATMs, a decent pizza place (Farina) and some useful chain restaurants (Le Pain Quotidien, Pret a Manger, Itsu, Paul). It's a 35-minute walk to the V&A if you prefer to be outdoors rather than take the tube. Kensington Palace, Holland Park and the Design Museum are somewhat closer than the V&A.
I believe the building was built as, and continues to be, housing for people taking classes at one or more schools, but the clientele includes people of all ages and rooms are often available for shorter stays. The rooms have private bath (shower) and are a bit larger than some of the severely cramped singles I've stayed in. This year's room had a mini-fridge; I can't swear that they all do. There's no air conditioning (and I'd hesitate before staying here mid-summer), but that would not be an issue in October. Wi-Fi has been reliable for me, but I always mention that it's important when making a reservation.
I was asked for a £100 deposit when my reservation was confirmed. There's no way to pay on the website, so I sent the credit card number in an email (yes, I know that is a tiny bit risky). I was in Poland at the time, and my credit card company blocked the transaction, so be sure to notify your card-issuer before making that payment.
At this time of year, with no air conditioning needed, I think this is one of the best-value places to stay in the city.
If you're flying out of Heathrow and are considering staying near the airport for your last night, check out the Premier Inn near T4, which is a 15-minute enclosed walk from the tube station. I booked several months ahead but paid only £37.50 for my room on September 9. The hotel is relatively new and the rooms are comfortable, though not particularly large.