Sorry, but James is talking rubbish - the East Anglia coast is not monotonous! Granted, the coast around Great Yarmouth isn't that exciting, but there are some gorgeous beaches on the North Norfolk coast, e.g. around Blakeney, Holkham etc. Take a boat trip out from Blakeney to see the seals.
Norwich is a good base. Airbnb tends to work out expensive over here - there are lots of holiday letting companies that have cottages, such as norfolkcottages.co.uk or sykescottages.co.uk. You could also try norfolktouristinformation.com or visitnorfolk.co.uk. Properties nearer to the coast will be more expensive. There are lots of caravan parks around Great Yarmouth, which would be cheaper.
There don't tend to be agents that find holiday properties for you, as Brits search online themselves.
By law, residential lettings have to be for a period of six months with a minimum 2 month period and the landlords take up references etc which is costly and many are unfurnished or partially furnished.
You may find someone prepared to grant a discount on a holiday property, but it sounds as though you will be there peak season, so your issues are that the best will already have been booked and they are less likely to give discounts when they know they can get full price.