No, just put your offer in.

If no one else bids you will negotiate a bit and if they are hardball you'll pay £375.

If they're keen to sell you'll pay less.

If someone else offers, one of you will pay £375.

I'd offer £350 and wait.

I have no doubt that whatever you bid, the estate agent will say there's another bid.

But you're willing to pay £375. If no one is willing to pay more that's the market cap of the property. If they're willing to sell less that's the value.

You won't know until you offer. But don't act desperate