estate agent got our offer wrong

[abouquetofsharpenedpencils]

Hello,
Please can anyone advise? I am a first-time buyer.
We viewed a house at £240k last Thursday. Owner is desperate to sell as the previous buyer pulled out at the last minute and he wants to have everything completed by the 30 September in order to avoid the stamp duty.
We loved it, put a formal offer forward of £238k on the Saturday.
We emailed this to the estate agent on Saturday very clearly stating £238k and our reasons for being a bit lower (20 year-old boiler).
Received an email from the estate agent 2 days later saying that our offer had been accepted.
Over the moon. Have since started the whole process of instructing solicitors, mortgages etc.
Today the estate agent tells me somewhere along the line there has been a mix-up and the owner never actually received our offer of £238 k and has sold it to us for 240k. He also said the owner will not consider anything under £240k.
He then said that after putting in my offer of £238k, I apparently rang back later and verbally increased it to £240k. I absolutely did not do this. We are borrowing maximum on the mortgage and are using every penny we can scrape together. Why would I do that if my offer had already been accepted??
It just doesn't make sense. I am feeling uncomfortable now and very stressed. If this is just a genuine mistake then ok, everyone makes mistakes, but why didn't the owner get our offer? I thought they were supposed to send our formal offer letter to them.
And the bit about saying I rang back and verbally increased it is just absolute rubbish. They have asked me if I can just pay the £240k but I am feeling really unhappy about the whole thing. It is their mistake after all, I have evidence in the form of emails stating the offer and amount and their email back saying it has been accepted.
I have no experience in this area and confrontation makes me feel physically ill. Can I contact the seller and discuss the matter with him? Or this is a big no-no? I would really like to know what they have said to him.
Apologies this has turned out so long. Thanks for reading to the end

Well done OP and well done on calling them out. It has been stressful but this was not of your making.

Now go and look online and look at all the things you can now afford with your £2k x

Why did you not tell them you'd spoken with the vendor and knew they were lying through their teeth?

I know you told them you'd be lied to, gaslit etc but you didn't mention that you'd actually spoken with the vendor so I wonder if you could throw that at the lying shits

When you have completed make sure you write this all in an honest google review of the EA.

Well done OP! They have messed you and the vendor around and I hope that both of you are able to complain in due course.

Oh my god, well done you!!! I’m so upset on your behalf!!!!

Good news. Now breathe. And then get excited! Congratulations.

Wow!
As if the house buying process isn't stressful enough.
Those EAs are either totally incompetent & trying to cover it up, or they were trying to cheat you.
Well done on getting it sorted out and I hope all goes well now.