The deposit is one month's rent and is not the last month's rent. Bills usually mean five separate things, each metered and billed on its own.
The deposit secures damage and unpaid bills. It is not rent, and using it as the last month's rent is only allowed if the contract says so. Agree in writing how long the owner has to return it and what may be deducted.
A Georgian flat normally has five running costs: electricity, gas, cold water, rubbish collection, and a monthly fee to the building's management for the entrance, the lift and the yard. Each is billed separately and most of them are metered.
"Utilities included" is not a defined term and different advertisers mean different things by it. Ask which of the five it covers, whether there is a cap, and get the answer into the contract rather than into a chat message.
Heating is the cost that varies most. Many buildings have no central heating, so the flat is heated by a gas boiler or by electric heaters, and a winter bill can be several times a summer one. Ask how the flat is heated before you compare two rents.
Internet is usually a separate contract with a provider, in whichever name the two of you agree. If the flat already has a line, ask whose account it is and whether it stays after you move in.
On handover day, photograph the electricity, gas and water meters and write the readings into the contract or into a short handover note that both of you sign. This is a five-minute job that settles almost every argument about bills before it starts.
This is a plain description of how the process usually goes, not legal advice. For anything that matters, confirm it at a Public Service Hall or with a lawyer.