There are three main types of material used in thatching in the UK. They are Water Reed, Combed Wheat Reed and Longstraw.
Combed wheat reed and Longstraw are both straw although the preparation and way the material is thatched differs.
The picture below identifies the materials. Left to right: Combed Wheat Reed, Longstraw, and Water Reed

Combed Wheat Reed:
Longer wheat or wheat/rye varieties than modern combineable crops and grown specifically for thatching for the length of straw rather than the yield of corn (maris widgeon, N59, triticali). Also grown with minimal nitrogen application as this causes the straw to rot prematurely.
Often harvested with a binder, then stooked in the fields for three weeks before being brought in. The grain is then separated from the straw in an old thrashing machine.
With combed wheat reed the thrasher has a 'comber' attachment fitted to the top of the machine.
Most straw is grown in the UK although some is imported e.g. Poland
Combed wheat reed roofs last approximately 30 years.
Longstraw:
Same varities as combed wheat reed and harvested similarly.
The main difference between longstraw and combed wheat reed is in the thrashing process. Longstraw thrashing machines do not have the 'comber' attachment. This means that as the straw is pulled through the thrasher it gets crushed.
As the straw is crushed it has to be prepared on the ground before it is ready to put on a roof making it a far more labour intensive way of thatching.
All straw is grown in the UK.
Longstraw roofs last 20 to 25 years
Water reed:
A wetland plant commonly associated with Norfolk.
It is cut each year by hand, or more commonally, with a 'reed cutter' in January/February. The bundles of reed are then cleaned by hand and retied before being baled into 60s or 70s for ease of transportation.
It grows to a height of anywhere between 3ft to 8ft with each size being useful somewhere on a roof.
It is the most durable of materials used and will commonly last approximately 50 years.