Amazon Prime delivery is not so fast as they say

Amazon is a big business and I was most of the times happy buying from them. They move fast, they sell good products and they have best customer service I ever saw, but... Even if I am paying for Prime membership, this Prime is not really giving me what it should. Prime means 1 day delivery and sometimes even evening delivery for some products if you buy early in the morning as they say on Amazon website:

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Delivery

Unlimited One-Day Delivery on millions of eligible items at no extra cost. Depending on the time of day that you place your order and your delivery address, if in stock it'll be dispatched that same day and delivered the next day. For more information on One-Day Delivery, go to About One-Day Delivery in the UK. For more information on Prime delivery options, go to Amazon Prime Delivery Benefits. Unlimited Same-Day (Evening Delivery) on eligible items to eligible postcodes at no extra cost. For more information, go to About Same-Day (Evening Delivery). No-Rush Delivery provides 3-5 business day delivery with a promotional credit. Learn more About the No-Rush Delivery Programme. Delivery Upgrades to faster delivery. Learn more.

Source: https://www.amazon.co.uk/gp/help/customer/display.html?nodeId=201910360

To make things clear, I live in London, UK so everything should be according to what they say but is not.

At least not all the time.

To prove my affirmation I will show you 2 orders I done in the last days.

In the first one it says:
FREE One-Day Delivery: get it by Tuesday, Feb. 13
when the order was done on 10 February 2018 as you can see from the right bottom corner. In this case, FREE One-Day Delivery means tomorrow but not on 3 days.

Amazon is doing wrong estimation for 1 day or evening delivery

On the next 2 images the delivery was estimated for the same day, on evening if the order was placed in the next 36 minutes as I actually done (basically in the next minute)

Wrong-estimation-delivery-amazon-prime

After the product was added to the cart, on the paying steps, the estimation was suddenly changed for 8th February 2018. Everything happened in less the 2 minutes.

Amazon-prime-wrong-estimation