This is one of the things often used as an example of how unprofessional estate agents can sometimes be. However, your agent is actually legally obliged to pass on all formal offers right up until contracts are exchanged, which is of course when the agreement becomes legally binding. Up to that point, your buyer is entitled to change their offer at any time – and by the same token, you are equally free to accept another offer.
Now, this might make sense in the case of higher offers, but why pass on lower offers? Well, in certain circumstances, a slightly lower offer may actually be in your best interests. For example, if you absolutely must move by a certain date and you’ve already accepted an offer but your buyer is trapped in a slow-moving chain, a marginally lower offer from, say, a cash buyer – someone who can effectively guarantee completion within your timeframe – may well be worth considering.
Practical and legal points aside, there is, of course, a moral argument to this rule – moving home is a big event in anyone’s life and once an agreement is made, most ideally wouldn’t want to renege on the deal and let the other party down. If you really are set on accepting a particular offer, irrespective of any others that might materialise, then you can always absolve your agent of his legal duty by confirming your wishes in writing.
At the end of the day, everyone’s situation is different and you have to do what’s right for you; if it meant your family was going to be homeless then you would have to do the right thing for your family, even if it did mean breaking a chain or letting others down. Given the choice, I’m sure we’d all opt for the more morally ‘right’ option if we could.