Get ListItem by unique value with c#

I try to get ListItem by unique value, as Mail. Every person has it's own unique mail address. I need to edit some of list data by looking up the Mail address and then edit items on this row. It is easily done by ID, but how to get ID with value?

It would be helpful, if this code can be written in C# not Query. If it is possible.

SPList

items = web.SiteUserInfoList;
SPListItem item = // Get item by unique value here. items.GetItemById(x) would return it by Id.