It might sound like a lot to people on small budgets, or people who don't really think about what money they spend, but it could be very easy for it not to be enough without appearing to have an extravagant lifestyle.
The OP says 'after bills, food and fuel' but before 'everything else so to go out and do activities, things for baby, savings, xmas etc'
So firstly it depends whether essential 'everything elses' like car insurance and repairs, home insurance, white goods replacements have been included in the bills food and fuel, or do they have to come out of the £500 - it's easy to think of this money as free spending money, but it's not really if you have a load of essential expenses that will crop up sooner or later to account for.
Then it sounds like there are two adults here, and the OP has already said that the money has to cover Christmas, baby activities etc. OK, none are strictly necessary, but if it's £250 per adult per month, that's less than £60 pw, or just over a tenner a day and there will be plenty of people who spend that or more, simply by getting a coffee on the way to work and their lunch in somewhere like Pret.
And we haven't even mentioned clothes for adults, or beauty treatments, hobbies etc. Again, there will be people who spend far more than £250 per adult per month on these things, you only have to look at the Style and Beauty board for proof of this.