All I can see is bracken?

Yes, not perhaps the best photo. The reed in question are at the right side of this photo, but have now taken over the whole burn. I will put up better photo on Monday.

The reed is probably Phragmites australis, a vigorous reed. Your burn seems to be very slow flowing so the reed could probably completely choke it given time. The reed is very difficult to control and digging it out is possibly the best option. I will finish with a link to a useful information sheet (American) but do not use the glyphosphate option without consulting the Environment Agency, England, or SEPA, Scotland first.
http://www.mass.gov/eea/docs/dcr/watersupply/lakepond/factsheet/phragmites.pdf

Thank you Bulbaholic, as you predicted burn is very choked. The burn is quite small but when raining in the mountains we get a "Whoosh" of water as you can tell by the flattened reeds. It will be quite a task to dig this all out, but looks like this will be the best option. We have recently acquired this garden, hence the question. Thank you once again. ?