Are you worried if your offer is accepted right away?

I assume you are willing to pay the offer price for the house, otherwise you wouldn't have made the offer. I also assume your contract stipulates that the house pass inspection and appraises for at least the contract price. If it does, you've just bought a house you like for a price you're willing to pay. If it doesn't you can back out of the contract or renegotiate the sale price. There's enough angst in buying a house that you don't need to stress over whether or not you've made the best possible deal.

Enjoy!

I agree with JPB. You would not have made an offer unless you meant it. You probably have no idea as to why the people are selling the house. Maybe they need the money quickly for one thing or another. Maybe they have already bought another house, and are pressured to make a deal quickly.

I don't know what is happening in England, but in the US, the real estate market is so lousy for sellers, that many homes are being sold at far less than they would have gotten just a few years ago. Sellers are happy to get an offer, any offer, especially if they are pressured to sell because of circumstances.

Be happy that you have a house that you want. Best of luck in your new home!

Maybe they just want to sell it.

Wait til the inspection and make sure nothing is wrong with the house.

Then get your keys and enjoy!