After 1837 there are the census and of course the birth, death, and marriage certificates to search and order. But if you are back beyond 1837, having reached a brick wall things become trickier. One needs to know where to look for the ancestor. It is, therefore, very useful to have found them first in the 1851 census, as this will give the springboard back as to where to look. The 1841 census only gives whether they lived in that county so not really much use. Watch out also for the "red herrings" of the 1841 census, as the enumerator was supposed to round the age down to the nearest five so 54 would be age 50, but some enumerators ignored this so ages can be a bit wild sometimes.
Another way of finding out where to look for ancestors is if you have a marriage occurring close in the 1840s, the marriage certificate will give and address for both spouses, and so that would be a useful indication. Using also banns certificates. The banns will say what parish both spouses came from. Or a marriage licences will give the same.
Wills can be a good source to kick-start brick walls. Maybe indication of brothers and sisters, or leaving money to other churches, so leading you to different parishes where the family may have originated. Also property in other villages or towns or counties. All worthwhile leads when the trail has dried up.
It goes without saying that the IGI should be checked and, latterly, the latest version of Vital records. It should always be checked whether the IGI has indeed copied the whole of that parish and not just a partial extraction. You can check that on the IGI's catalogue. For instance, sometimes it's only the Bishop's transcripts and not the parish register on the IGI. Equally, there may be just the parish registers and not the Bishop's transcripts or BT's as they are known, on the IGI. So a checking of the BT's should be done.
What are the BT's? After 1598 it was ordered that each year all the baptism, marriages, and burials were listed and copies sent to the Bishop of the diocese who oversaw the churches. It's hit and miss, though, whether BT's survived or not. Each parish is different. The interesting point here is that the Parish register and the Bishop's transcripts although covering the same year and the same events can have extra things added or omitted and also variations of name spelling occur. So both sources should be checked.