Hi Toberwine, thank-you very much for taking the time to write such a useful and comprehensive reply.
I can hardly believe two years have passed since I started this thread!
You are correct that the deer numbers are definitely a factor in the increasing dominance of the pendulous sedge. I think in our case by browsing out competitive plant species, I think in our case mainly bramble.
We have huge herds of Fallow in the area, it's not uncommon to see groups of does between 80 and 100 on surrounding farmland. Muntjac also are increasingly present and their increasing numbers seem to be resulting in making them less territorial. In an area where 5 years ago there would only be a single pair there now can be 2 or 3 pairs.
In the last two years however progress has been made in starting to control deer numbers as my immediate neighbouring farmer has brought in a professional stalker and between us approximately 130 does were culled in the first season and this past season I think nearly 100. I have to admit my contribution was only in single digits.
So overall deer numbers are down but still too early to see any environmental impact.
My other finding echoes what you say about cutting back being beneficial. We have an area that would once have been part of the outer reaches of the estate gardens which had been heavily planted with daffodils. These were becoming badly suppressed by the sedge and so about five years ago I started mowing this area in the autumn with a large pedestrian mower/brush cutter. I've been convinced this winter/spring that the sedge in this area is starting to reduce. The sedge plants don't seem to become mature enough to produce flowers and I'm sure this will have a long term effect as well as just general debulking and exhausting the sedge resources.
Interestingly in this area another plant is becoming more dominant. Tutsan (Hypericum androsaemum), another plant that the deer won't browse.
This year for the first time I can recollect the deer have eaten off all the daffodil flowers, not just in that area but over the whole estate.
I'm thinking of extending my mowing experiment in other areas, probably by getting in a flail for the tractor or possibly for the excavator although I think it's probably a bit too light and old to cope with the high demands of a hydraulic flail.
Regarding glyphosate, we have not had much success with it in our garden, adjacent to the woodland. I think where it might be of value is in controlling seedling sedge plants early in the year possibly after mowing in the previous autumn.
To be honest the invasive plant control has been put on a back burner for now as I'm up to my eyes dealing with Ash die back and its consequences. Thanks again for your reply.
All the best
Alan