You are allowed to 'express a preference' but the LEA's wishes are paramount
That is a bit of a simplification to say the least. The LA (local authority) cannot simply ignore your preferences and allocate schools the way they see fit.
Every school has an admission number, sometimes referred to as PAN (Published Admission Number). This is the maximum number of pupils who will be admitted to year. If the number of pupils naming the school as a preference is less than the admission number they will all be admitted. However, if there aren't enough places at the school for all the applicants the school's admission criteria are used to decide who gets in. In general all the community schools within an LA will have the same admission criteria but other types of school (faith schools, foundation schools, academies and free schools) can set their own criteria. The admission criteria will specify who gets priority for admission and what tie breaker is used to determine who gets a place between two applicants of equal priority. Distance from the school is the most common tie breaker but it isn't used universally.
Most people get a place at one of their preferences and a high proportion get their first preference. However, there are always some people every year who don't get a place at any of their preferences. The LA must then allocate a place elsewhere. This will usually be at the nearest school with places available, but that may be some distance from home. It is therefore important to use your preferences sensibly and include at least one school where you have a very high chance of getting in.
The LA co-ordinates the whole admissions process. You apply to them for places. You will be able to name at least three preferences - some LAs allow more than this. You will only receive one offer from the LA which will be at your highest preference where there was a place available. So if there were places available for your child at your first and third preferences you will only be offered your first preference.
English schools are all Christian
Just to clarify that remark, a significant proportion of state schools are church schools, usually CofE or RC. There are also some schools of non-Christian faiths, although these are comparatively rare.
All schools are required to have a daily act of collective worship. For non-faith schools this must be wholly or mainly of a broadly Christian character. Faith schools can do whatever they want in their worship. In practise many schools, including faith schools, ignore the requirement for a daily act of worship completely. Even when there is some form of assembly it frequently does not include any worship and has little or no Christian content.
Religious Education forms part of the compulsory syllabus for children up to the age of 16. RE in non-faith schools is supposed to reflect the fact that religious traditions in the UK are generally Christian but should also take account of the other major religions. Faith schools can set their own syllabus for RE which can include more or less about Christianity than non-faith schools. A significant proportion of schools ignore the requirement to teach RE completely.
Some church schools are not very religious. Some non-faith schools are very religious. Parents have the right to withdraw their child from RE and/or collective worship, although very few parents exercise this right.