Where you live will impact how much you will be paying for your insurance policy, for example if you live in an area with a high crime rate or high flood risk, the likelihood of you needing to claim is a lot higher than usual.
Terraced houses, flats, detached, semi-detached, coach houses are all priced differently and the size of the house is a key factor. If your property is bigger, it will be more to insure as the rebuild cost will be higher.
If you also have multiple bathrooms this will also cause your policy to be higher as you have more pipes that could possibly burst and cause water damage to your property. Insurers typically pay out more claims due to damage caused by water than any other type of claim.
For accidental damage, the more people living in the property the more people that may accidentally cause damage and therefore the more you may need to pay.
Any insurer will want to know your previous claims, most will ask for any claims within the last 5 years. You will receive a higher discount the more no claims you have, just like car insurance. Although it may feel convincing to not share this information however, it can be seen as fraud and could mean that if you did claim on that policy it would be declined due to non disclosure which is not worth the risk for a slightly higher premium.