Can an estate agent refuse an offer that is "too low"?

I believe they are obliged to report it to the seller. The seller may have made it clear that they won’t entertain offers below asking though.

If you put a low ball offer in that is clearly well under the current value of the property, why on earth would the agent waste their and their client's time even reading the offer.

If a property if on the market for many months, there may be a case for it

seller can have told them not to accept anything under the asking price

It absolutely is.

How do you know the asking price is realistic, even in today's market?

Estate agent should be passing on all offers to the seller. They can be rejected in two minutes.

Op you're about 10 years too late, unfortunately the days of offers below asking price being entertained are a distant memory. If you are genuinely interested in the property, 5-10% over the asking is probably a good starting point these days. It may seem counterproductive, but it's a tactic that can short circuit a bidding war early.

That depends if you think the asking price is reasonable in today's market.

No. There’s no requirement at all. Some sellers want to be kept informed of everything. Others don’t.

In current market anything under asking isn't going to be entertained. Estate agents favourite game is to put asking price way under what they know it will sell for to get people interested. If you want to be taken serious as a bidder understand the market and bid accordingly.

And other agents put up properties with an "asking price" of what they hope to get which may be very aspirational and would consider sums below the "asking". Different tactics by agent. If you're watching a market you can usually suss which agents price keenly to trigger bidding wars and which agents price high.

OP should make their offer and ask to be kept updated of any further offers and keep looking elsewhere and not get het up on the legalese of agents forwarding offers.

It is a private sale of a piece of private property. They can essentially do whatever they want. They don't owe you anything, they don't have to be transparent, nor have to explain themselves to you. They don't even have to pick up the phone to you if they don't feel like it.

If it was a public tender for a public service or a piece of property owned by a public body, it would be very different.

It's possibly a function of the market where I am - lots of identical apartments and houses with plenty turnover so the market price is readily obtainable off the PPR. I expect the psychology is that both parties know the "market value" and the seller is trying to cajole a few more quid out of the buyer (ie shame them into going say 95% of the "asking" which may be 5% more than recent sales). I've noticed that the agent who's first name rhymes with a fruit tend to have higher askings than the smaller or local agents around me anyway.

Or else some agent's business model is tell the vendor a large market value to get the listing in the first place. I'd expect at the lower end of the market, agents price the properties keen to capitalise on market FOMO of buyers in that market segment.