Letting Agent proposes relative to rent my house

I agree with your instinct, and I think in your shoes I'd make it an "either / or". In other words, say to the letting agent "I am happy to rent the house to your family member, but on the condition that I switch the management of the property to another agent (at another management company) to avoid the conflict of interest that would otherwise arise."

On the plus side, the agent has at least declared this situation to you - presumably she could have just not mentioned that she happens to be related to the proposed new tenants. You should thank her for that and perhaps explain that you will switch the property back to her management once her family members have moved out in the future.

It is possible that the company they work for won't allow this. Taking money from the property owner to represent them, but then potentially helping the tenant could be against their employment contract. Their boss would not be happy about losing a customer because of this.

Yes this is a conflict of interest. Assume the fee they collect is 1/2 of a months rent per year. If they can save their relative £100 per month or £1,200 per year on the rent it will only cost them £50 in fees. Of course if you drop them they will miss out on the entire fee.

That conflict extends to all disputes. They could push for you to buy a new carpet, or pay for a repair that is the fault of the tenant.

I don't think there are any safeguards you can put in place. That is why many companies won't allow it. The chance for bias is there. The question is how they can now prove that they won't hold a grudge when trying to find you a tenant.

As others have said, this is a clear conflict of interest.

US rules for real estate agents (for sales rather than renting, but analogous situations could arise there), have two solutions to such a situation.

Solution 1: You make the situation explicit and change the relationship with your agent. In the analogous situation for real estate agents, you would make three changes. First, you would agree, in writing, that the agent represents both parties, rather than you. Second, the agent collects only half the fee from each party. Third, the agent is in this situation ethics-bound to not act in your interest, nor in the other party's interest, but act as an unbiased judge would.

Solution 2: The agent hands of one of the two parties to another agent (usually from the same firm) as soon as the problem becomes obvious. That is, of course, the option all the other answers also offered.

Usually, the listing agreement includes language that Solution 1 automatically kicks in when appropriate.

In practical terms, agents usually won't allow that to happen, though, because it cuts the agent's earnings in half, and also because it can become a minefield.

But it exists as an option, if you really wanted to go that route.

Kudos to your agent to disclosing the issue and working with you on it. It looks like she is trying to do the right thing but unsure herself how to navigate the situation.

It may be not that bad.

If you have a history of good business with the firm, a tenant that is related to the Agent has rather small potential of things messing up. Maybe, just do everything as usual.

The disclosure of the conflict of interest is good. Your agent could as well not tell you that they are working with close relatives and just close the deal. Or disclose the fact afterwards.

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I don't know how the property rent market looks like in UK, but in a lot of other places it is quite unusual right now. Rents are going low here, a lot of properties stay unused.

It may be as well that the agent is doing you a favour.