Married couples often think the survivor will get everything even without a Will. This is simply not the case. The Government sets the level that the survivor is entitled to, this is known as the 'Statutory Legacy' and depends on whether there are children involved or not.
The best way to ensure the survivor inherits quickly and with as less hassle as possible is to make a Will.
A marriage cancels a Will which could result in the new spouse inheriting everything. Upon death, it would be their blood relatives that could inherit everything and the original children could end up with nothing.
However, by ensuring the property is held correctly, then each half of the house could be put in a Property Protection Trust Will for your children. This will help make sure they inherit your half even if the survivor remarries.