Did you post in the hope of getting lots of PMs of potential clients? People are telling you the problem, you're dismissing them and preferring to listen to pie in the sky types who swear blind they never pay a penny less than £500 an hour because children are the greatest gift of all.
Take note that if these people were your target market they would have booked you by now. It's not whether the product/service you're offering is worth it, it's whether people who need that service will pay it to you for that service at this point in time. Obviously that's not happening or you wouldn't be here.
You're not going to listen because you haven't listened to anyone else saying the same, but I'm just outside London in one of the most expensive parts of the UK outside Z1/2, and £11 an hour is not far off nanny money, certainly on Childcare.co.uk. I just wouldn't pay that for a babysitter who for my under 5's would start after they were in bed, and who isn't actually supposed to meet specific outcomes every session with my children or take them anywhere and who isn't paying NI/tax/insurance/car costs on top of that to do things with my kids. Or even talk to the children as they're asleep.
On top of that, even if that was the going rate (which it isn't), I don't have the money for that plus overpriced food/drinks so I accept that I can't go out in the evening, it's part of having kids. Many people around here have had mortgage increases of over £500 a month. They look like they're doing well from the outside but they're really not. They're not going out either and I can only imagine how much tighter their budget is than ours.
If I need extra childcare for any reason, I ask my childminder who is £6.50 an hour (and offers sibling discount) and make sure I only make plans during the day when she's available, or I do things I can take my kids to.
There are a lot of people in a similar boat, and £11 an hour is fantasy money for a babysitter in December 2023 unless you are established and have loads of warm contacts of wealthy parents who might want your services (which you clearly don't or you wouldn't be posting).