YANBU to expect the pub to let you in with a baby- most do these days, unless you're in Scotland?
In Scotland you need to apply for a special licence to have children in the pub, and many don't bother, meaning the pub is strictly 18+.
In England and Wales, the most pubs are licenced to let children in. Social attitudes have changed and with them licensing laws (not that you'd know it from this thread
) although many pubs do still have older licenses that don't allow for children. Then there are also the landlord who simply don't want children in the pub, so it's best to check, but bit unreasonable to expect babies to be let in.
The law says that children under 16 can go in pubs, they must accompanied by an adult if it's a venue that primarily serves alcohol, and it's illegal to have them there between midnight and 5am.
In practice a lot of pubs will ask children to leave at 7pm or 8pm although lots will make an exception for a babe in arms especially if you're there having a meal.
I spent a lot of time with my ante natal class friends, hanging out in a local pub in the daytime as it was a lovely space - large comfy sofas, huge windows you could watch the world go by in, nice food, great baby changing facilities in the toilets. In the weekday daytimes, when we'd meet there, we often were the only group of paying customers and the pub were very welcoming.
It once occured to me that only a few generations ago, women wouldn't have been allowed in the pubs at all, as a rule, and I imagined grumpy old men saying "you can't let the women in, next thing they'll be wanting to bring their babies with them!" And then look around at all of us there with our babies and prams, taking over a while section of the pub smile. Progress 
AIBU is full of people who like to have a go at the OP, especially if they can pick at you for breaking a rule.
But out here in the real world it's perfectly normal to go to the pub with your baby. Heck, I had my eldest's first birthday in our local!
Try posting in your local Facebook group to ask which pubs will allow babies in.