That sounds like quite a lot tbh, we live in a similar 3 bed semi and our winter bill (december-march) was about £200, our dd for the gas is £47 per month, which is a little high as we too were paying off a previous bill in the first year. The past winter we had the heating on quite a lot with it being so cold, we don't leave it at a constant temperature though, we turn it on and off manually (thermostat is opposite front door, so always reads low).
Our gas bills for the autumn period are generally about £100-£150 per quarter, winter £200-£250 and the 2 spring/summer ones are generally about £40 per quarter.
Our hot water is provided by the gas immersion heater too, is your hot water included or electric?
We are generally in credit with both the gas and electric within the last year, prefer to leave it like that though, saves anxiety about switching the heating on.
£360 a quarter is a large amount just for gas, are you giving in readings? We are with edf who have just raised prices and introduced a standing charge, a bloke in M&S collared me in the winter looking to change suppliers and said that edf was good value but look at M&S when they raised prices, just about to do that.