The letting agency are quite within their rights to put a 'no children' clause into their letting contracts. They're not all the same, though, so shop around. We have rented for a number of years now, this being our second property - both times, we have gone via the same letting agency. When we began we had two kids and two dogs and still found a decent house.
Our letting agency is purely that - they specialise in rented property only and belong to a 'trade' body with a specified code of practice - as opposed to being an estate agent that also lets property.
Please don't be put off. Keep looking and you will find somewhere, I promise.