It much depends on the number of people expected, and for how long you want the celebration to last.
£2K isn't necessarily expensive if there will be a great many people: 200 people = £10.00 per head if they are drinking and eating VERY moderately...
It is usually cheaper to reserve an area within a bar/pub rather than a separate room or whole bar, put a fixed amount (whatever it is you can afford) behind the bar and it's free drinks for your guests until that money runs out. After that moment, each guest has to pay their own way.
In January trade will have slowed down considerably compared to the festive season we are now undergoing, so you are more likely to find landlords more accommodating than they are right now.