Is there a risk of localised die-off when plants bud too early?
If you're talking about shoots or buds coming out of individual seeds, then those plants are probably doomed. Most seeds are "designed" as one-shot delivery packages. In this case, they'll bud, be killed off by a frost at some point during the winter, and then be spent.

For a perennial plant like a tree that buds year after year, the impact of an early blooming will depend on the species. As per a Q&amp;A from Cornell (Will Warm Winter Wither Plants?, 2007), most plants growing in a temperate climate (like that of Britain) will have experienced warm winters before and will have at least some evolutionary adaptations to help them deal with occasional aberrant weather. For example, even if you do see some fresh buds on a tree this time of year it is likely that the majority of its bud primordia (the parts of the plant that will someday become buds) have not developed. Although you won't see regrowth in the spring of most of the buds that opened early, you will see normal development of the buds that stayed dormant during the winter.

As for the question of wider ecological change, one anomalous year isn't going to make a difference because, as you say, a large portion of the seeds/shoots/buds/whatever refrain from growing even if some are being tricked by the mild winter. However, if a string of mild winters cause significant die-off year after year you would start to see changes in the ecosystem. It works the same way for many with loosing their hair...