Where do I stand with letting agent as Landlord

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My husband and I are moving abroad so will be renting our house out. We haven’t signed anything with the letting agent however they have marketed the house and found a suitable tenant.
Over the weekend a friend has asked to the rent the house from us (we will draw up a contract and make sure it’s all done properly).
Do I owe the agent anything for their work despite the fact we never took on the tenant or signed a contract?

Yes
You will have entered into a verbal contract with the letting agency.
The agency is a business it did not pick you out at random and decide to advertise you house for rent.
You are in contract and bound by whatever terms you agreed to.
The agent was foolish not to ensure that you has signed the paperwork as it would be much more difficult to prove the T&C.

You owe the costs involved in location a person willing to rent your house and what ever other costs you agreed to

PS it is risky to do business with friends as you can loose the friend along with rental income and costs to evict too.

I would reinforce the warning about letting to a friend. DB rented to the daughter of a friend and it was a nightmare, taking in lodgers, damaging a fireplace by painting in black, damaged doors, not paying gas bill. He rented it excluding his separate garage and they broke in and removed some items.
He asked them to leave and her mother didn’t speak to him again.

I would absolutely put everything in the hands of the estate agent, let them find and vet the tenants, do all the correct legal paperwork and manage the deposit. you will be abroad, you need everything done properly.
If your friends want to rent, ask them to contact the estate agent.
The law around rental properties is complicated and everything needs to be done properly.
There was a thread on here a few weeks back where the property owner had allowed friends to stay in their property and the "friends" had refused to move out. there was nothing they could do because they hadn't followed the correct legal procedure.

From abroad? Use the letting agency. You will need someone on the ground.

Letting to a friend isn't a great idea. You risk loosing the friendship as well as the rental income if it goes wrong

As an aside, how does the friend know? Because of the agency marking???

I'm a LL and I'd suggest advising your friend to apply through LL as you won't be in the country to deal with any issues.