This really comes down to several things.
First, how close the offer is to the amount you expected. If it’s far off, it’s probably worth keeping it on the market to see if other offers develop.
If it’s close to your expected price, it’s a brave person who turns that down in the hope of finding something quickly. A bird in the hand, after all…
This must of course be balanced with the second question; how urgently you need to move. If you’re in no hurry but want to get the best price, then it might be worth staying on the market to see what else develops. If you’re keen to move soon (perhaps before a certain date, or you’ve fallen in love with another property) then accepting might feel like the safest thing to do.
Dare I say, but it also comes down to how much you trust your agent, and the advice they would give you in this instance!
If you chose them because they were the cheapest or they flattered you with an over-blown valuation, then you may might feel doubtful about the quality of their advice. Agents who routinely overvalue are not being strictly honest with their clients at the very outset and when it comes to lower fees, well you generally get what you pay for!
If, on the other hand, you chose your agent on the basis of their professional reputation or through personal recommendation – then you might feel more inclined to accept their advice.
Of course, you can always try hedging your bets by accepting this first offer while keeping your home on the market. After all, under the English system nothing is legally binding on either party until exchange of contracts. But I would be very cautious about doing so, not least because your agent would be obliged to inform your buyers of the fact, in writing – and you could end up losing them.
It’s also wise, in somewhat turbulent times, to remember that we never know what’s around the corner – personally, locally, nationally and globally. Sadly, history is littered with people waiting for a better offer, only to see that turn to tears when the unexpected happens.
It’s common in a ‘quick offer’ situation like this to think both you’re your agent has done nothing for their fee and/or that it’s priced too low and raising the price would deliver a higher offer.
But take a step back and think about your objective: probably to get your house sold for as little hassle as possible. If you get a good offer without having to endure endless viewings, and this enables you to start looking for your next property with a firm offer under the belt and a clear budget, it’s a brave person who turns their nose up at that!