Do disabled carers usually pay for normal tourist sites?

Well, the good news is that many prime attractions in London are free (British Museum, National Gallery, Victoria and Albert Museum,...a big list) so fewer issues. For other sights you might be interested in (Westminster Abbey, St. Pauls, Tower of London, Churchill War Rooms) I would take a look at the website, for what we refer to as Handicap, they may refer it as a "Concession" which includes Seniors, the Disabled, sometimes Students. Caretakers are not always mentioned, it might be worth emailing to ask.

As for any other accommodations, some validation of a disability might be handy, I know with Parking, there is no obligation to honor a permit, but they often do, so if something requires an "official" validation, it might be hit or miss.

Check up the website information as most sites will give their concession policy. Often it is the person with disabilities that pays for entrance (sometimes at a reduced rate) and the carer is free. More rarely both are free - or both pay ...

As Marco says, you should not "wait and see," but instead should look at websites now. And as Paul says, the UK term for what you want is "concessions." If any of them are unclear, you can email them for exact details.

Note that the London Pass is hard to make pay off, unless you're running around a lot. Also note that it touts its "skip the line" benefits, but you only get these at six attractions:

Tower Bridge Exhibition
St. Paul's Cathedral
Hampton Court Palace
London Zoo
London Bridge Experience
Kew Gardens

As has been said, many attractions don't charge admission. Of those that do, almost all now have discounts for advance online booking. The trick I learned is, for most of them, the morning of your visit is far enough "in advance." So, for many things, and assuming you're traveling with an internet-enabled device, you can just figure out what you're seeing that day, and book it using the hotels' Wi-Fi before you leave. For some, the ticket must be printed (or else you have to wait in line to get a printed ticket by showing your confirmation email); for others, the ticket can be scanned off your phone or tablet.

An exception to booking the morning of visiting is the Churchill War Rooms. While this is covered on the London Pass, it does not give skip the line privileges. And due to the movie The Darkest Hour, the lines here can be very long. So, if you want to see this, you will want to pre-book timed tickets; as a bonus, this is also cheaper than waiting in line to buy tickets.

In my non-comprehensive research, some other major sights that had a discount of £1 to £5.25 for online advance booking are:

St. Paul's Cathedral
Kensington Palace
Royal Observatory Greenwich & Cutty Sark
Westminster Abbey
Tower of London
London Transport Museum
Kew Gardens

An aside about "free" museum admission in the UK. The policy is generous, until it comes to the often-spectacular special exhibitions. They are the ones that draw line-ups and charge fairly stiff admission. Often the tickets can be bought in advance, perhaps with a time for admission.