Agency told me that I need to give my meter reading to the neighbours downstairs but their electricity bill is top-up. Any suggestions?

Hey, welcome @K_Liliana !

We’ll need some time to think of how best to answer the agency question. But for now, please feel free to take a look at an existing thread for a long-term solution. This is the safest way to get separate bills for each flat.

While you read that, we’ll think this one through.

Back soon! :)

With any flat the best answer has to be a seperate supply and meter for each. Sharing a metered supply with a sub-meter is likely to cause problems with disagreements likely to arise. To get seperate meters however it is likely to involve both the energy supplier and an electrician to seperate the supplies to each flat. It would be worth looking at the cost of doing this as it may not come cheap if an extensive re-wire is required.

Who's name is the account in with the provider, your neighbour or the LL/agency?
Who do you pay?

Seperating the supply so there is one bill for each flat will cost your landlord money. (Which is likely why it hasn't already been done).
You should note that that may result in an increase in rent for both flats.

On a landlords forum I frequent you see many such posts about 1 supply/billing for houses that have been converted to flats without the utility supplies being fully split.

Your particular LL appears to have gone the half-way method of getting a private electricity sub-meter installed, so that at least you can see what the sub-flat uses and deduct that from the total billed for the property.

It isn't ideal at all, but better than nothing.
You have to calculate your own usage cost based of kWh recorded on the sub-meter plus a proportion of the standing charge.
(And it threw up some interesting arguments with last years energy discounts applying to the billed account only).
The fact that it's now a top-up meter for the main supply is just a further complication, I suspect it wasn't one at the time of the conversion.

However that is a better situation than where the LL has not installed any sub-meter and everyone is then left guessing/arguing who used what, and the bill payer trying to get the money from the non-bill payer(s).

A 3rd option is just to split the bills equally between each flat, that also usually leads to argument.

The 4th option is for a LL to rent out 'bills included', but many got stung when the energy prices rocketed up and they couldn't simply raise the all-inclusive rent to match. It was a particular problem in student accomodation where fixed rents can be agreed up to 12 months in advance.
So many LLs are now wary of that option.

PS. I assume that you also have a similar arrangement for the Water bills, and any gas supply.