Who is responsible for maintenance fees on a rented property?
No it seems like they are taking liberties. You are not directly responsible for any ongoing maintenance to the property or grounds, your landlord or their agents are. You will already be paying for this in your rent and it sounds like the estate agents are trying to get you to cover something they should be speaking to the landlord about. Speak to someone at your local Citizens Advice Bureau if you can, or alternatively your local council should also have an officer or department (usually housing advice) who can help you.
Your lease / tenancy agreement will specify who is responsible for what. Anything not expressly mentioned as being your responsibility is down to the landlord. This kind of payment is definitely not considered a utility bill. In short (eg monthly or 1 or 2 year fixed term) leases it will almost certainly be the landlord who has to deal with these things, and the rent will be set at a level that includes the landlord’s expenses. In longer leases (many years, often refered to as leasehold) the tenant is effectlively the full owner and is likely to be responsible for these sorts of things. However, the landlord might retain responsibility but will be able to levy a service charge to recover the cost from you.