Hi Beeper!
Pretty much everything has been covered by everyones responses. Just to give you some other elements,
1. Depending on your individual circumstances, having your possesions insured is optional but highly recommeded, even if it's for accidental damage that you may in the future need to claim. I rent my flat/apartment out and it's on the ground floor of a purpose built block, and I've stressed to tenants to take out insurance as it's 'relatively' easy to break in. Indeed, there have been attempts and one incident where they actually got in, but we suspect that was down to one of the renters having some sort of vendetta. If the flat you rent turns out to be 1st floor and above, you'll enjoy a cheaper premium as well (less risk of break in)
2. The only other 'cost' to you will be getting items to keep the flat/apartment clean as per the contract you'll sign. Figure those costs into your budget(s) for the month/duration of your stay.
As already discussed - if you speak to an agent or a private landlord, ask to see the meter to get readings on the day of you moving in or an agreed time. Once you have that information, you can call up the utility company and quote that figure and they'll look after the rest. I think it is possible to switch suppliers even if you are in a purpose built block of flats etc as the bills will be in your name, check the usual comparison websites for that. Also, some flats may or may not have a Gas supply (my flat is all electric for instance) so factor that in as per your (possible) cooking preferences! - lastly in relation to this, all your costs could vary as you haven't as yet decided on a town/city or region of the UK you'll want to be in - South east and London are of course the most expensive areas overall !
All other costs will be primarily optional to you and your individual lifestyle!
Hope the above helps! cheers! DtM! West London & Slough UK!