Narrowed down to a few options - offer one at a time, or all at once?

Don't offer on more than one property at a time with the same estate agent. But otherwise I think it's OK to make multiple offers. Especially if you put in low offers, which are likely to get rejected. That can be useful (e.g. if one just says "no" and another gives a counter, or at least a suggested increase, that will help you decide what to do next).

I’d offer on the proviso that if they accept they take the property off the market immediately because there are other properties you’re considering too. Just because a seller accepts your offer doesn’t mean the sale will go through. However, if they’re willing to consider taking the property off the market then that’s an indicator that they’re serious about selling too.

As a seller, I’d be pissed if the buyer offered and pulled out for no reason apart from “I found something better”. This isn’t some trinket on Amazon they’re flogging. There’s a lot bound up in the sale for them emotionally as well. I’d urge you to consider their side. Treat them as how you would like to be treated.

Out of curiosity, are you a first time buyer?

I would 100% offer on all three so long as they weren't with the same estate agent. You owe them no exclusivity because they owe you no exclusivity. If any of them were with the same estate agent I'd call up and try to get a feel for if they would view multiple offers as an issue.

They may even give you a hint as to whether one of them already has an offer that's likely to be more attractive than what you were thinking. They will also probably give you an idea of the time frame involved. Here it's not uncommon for places to set a best and final deadline 5 days out. That'd leave you time to see how you get on with the others.

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Offer on one at a time, but you can say you're also interested in other properties and need to know as soon as possible.

We were selling and accepted an offer only to find out the buyer had made multiple offers and wanted time to decide between the properties who had accepted his offers. Meanwhile, while he was deciding, our estate agent encouraged us to keep doing viewings and the following day we received a better offer and accepted it as we could tell they were more serious about buying than the other buyer.