Londoners in particular. Is 40k Pounds a year enough money to live a cool life in London?? I know this is vague question! But in general ? obviously more would always be better!! but in general! hahaha

It is enough to live comfortable. Define cool. If you mean eating at the Ivy, then no. If you mean going out e time a week to where regular people go, then just about enough.

Are you including rent? That would eat up a chunk of your 40k.
Travel in and around London might cost 2-4k, as well.
Food + entertainment.... sky's the limit.

No, does not including anything! the job pays 40k gross .....what does a apt cost in London? Don't have to be in the main area but not in the suburbs either.

You can check rents here, www.rightmove.co.uk.
You can search by distance from a place. e.g. within 5 miles of Chelsea

I think it's decent for London. Not too low and not high.
London isn't cheap, but it depends if you have a small apartment or if you move there with a family. I think you can find places in your budget if you're by yourself. 6 Most important things: 1. check where the nearest tube/metro lines are if you need them for going to work. Check the area and how safe it is (google maps has street view). 3 Buy your food at Tesco. (Check if there is one nearby your apartment as that saves you a LOT of money if you cook yourself). 4: bring your own lunch to work and a snack for the way back. Lunches add up quickly and sandwiches are not cheap. Why a snack for the way back? In case you get delayed in traffic/tube. 5. Bring water in case you get stuck in traffic/tube (very very important). 6. Get an Oyster card (for overground district trains and metro, tube and bus)
Fine dining is very expensive usually. If you're young and just want a fun dinner with friends, then there are also places that suit that. Wetherspoons or Lloyd's have decent foods and combo events (drinks and food platters)
Just some suggestions :)

Lived in London most of life and yes 40k will give you a decent life. Social life, rent, food should all be good enough with that!
Think average Londoner is on 25k!!!