The website for Hampton Court, Kensington Palace, etc. show 2017 prices through February 28. Do prices normally go up for the summer?
Kensington Palace website show prices....1 March 2017 - February 2018 adult £19.00 gate price, £17.10 online price, child under 16 free.
Hampton Court website shows prices for summer 2017 £18.40 per adult, child £9.20., family £45.40.
You can buy your ticket for Kensington Palace for dates March 1, 2017 - Feb 28, 2018 for GBP 17.10 on line, it is more if you buy it at the gate. The prices went up as of March 1, 2017 but remain the same until Feb 28, 2018. I bought my ticket on line, no issues.
Buckingham Palace ( which I know you did not ask about) is not on sale yet and is only good for Aug through Sept 2017 as it is not open to the public any other time.
I just returned from a London trip last year. Depending on the sites you want to see and how many people there are I would think about getting a pass from the Historic Royal Palaces.
The Historical Royal Palaces (http://www.hrp.org.uk/) has Memberships. The even sent my packet to the US. It does take, I think over a month maybe two, and they send you cards (like a credit card size) and its good for a year. I used it to visit Hampton Court, Kensington Palace, and the Tower of London. I did save a bit from the gate price but you might want to do the math yourself since I didn't look at the "online" price. You can visit these places as many times as you like. I went to the Tower twice as it huge and I got tired fast.
Also I can see where susan is confused. When I went to the Historical Royal Palaces site and clicked Hampton Court and under Visit Us - Tickets and Prices it does only seem to have through 28 February 2017 in table format.