Your agent wants you to take the offer precisely because you are in no rush to sell, it’s costing them money to advertise and chase up viewings etc.
I think average time from offer to completion is ~4 months. Add in Christmas and a buyer should be looking at having their offer accepted by the end of October if they want to ensure they avoid the stamp duty.
The stamp duty on a £400k house will be £10k when the rates revert but I don’t think that directly equates to the amount it will affect sale prices. Buyers will either need the extra £10k as cash or they take it out of the equity in their current property (assuming they have one) – if that’s the case, it could affect the mortgage LTV and disproportionately impact their ability to afford a house.
No idea what area you live in or the desirability of that type of property in that area, but here (Cambridgeshire) homes have been selling fast. The really desirable stuff goes in days and even the ropey stuff has gone in 4 weeks tops.
An offer of £365k sounds like a genuine one. Did you counter offer?