Ah congratulations, a very exciting time. You offer whatever you think the house is worth, I am of the view (both when buying and selling) that there is no such thing as CFery in the house buying world, there is no relationship between you and the seller, you don't 'owe' them anything and certainly you don't owe them what they think their house is worth.
It can be hard especially at first to gauge how much a house is worth but you will start to get a better feel after the first few houses (this is why convential wisdom says never buy the first thing you see) and you can use Zoopla etc. to look up what average prices in the area are and what similar properties on the road or neighbouring roads have sold for recently.
It's reasonably normal buying etiquette to make an opening offer at somewhat less than what you think the house is worth in order to give you some headroom for haggling, but whether that's £1000 under, £10,000 under or £100k under really depends on loads of factors, how much the house is on the market for, how long it's been on the market for (if longer there is usually more room for negotiation), market conditions in the area, what you can afford, whether there are any other bidders in the running and also the circumstances of you as a buyer and the seller, so for instance if the seller needs to move quickly and you are a cash buyer you can usually use that as a negotiation point for a small discount. As FTB who (presumably?) need a mortgage you are not in quite as good a position as a cash buyer but next best thing as you're not in a chain...
I would be vague with the EA about your max. budget when just viewing, they work for the seller not for you remember so don't give them any advantage in negotiating. But of course if you are offering your maximum and can't offer any more then say so.
Any more questions do ask!