It's important to note that (in general) sellers pay the estate agents fee and buyers pay stamp duty. If you are both buying and selling then you'd pay both, but on different properties. However if you're moving to/from rentals, dead or moving abroad then you'd pay only one.

Also it's possible to cut out the estate agent if you really want to save money. There are a bunch of websites that for a minimal flat fee will let you DIY it, but be prepared to make your own for sale sign, photograph your own property, and show prospective buyers around.