http://www.thelancet.com/journals/lancet/article/PIIS0140-6736%2813%2962301-6/abstractThis is the study referenced in the BBC features.
Eligible participants were aged 7—16 years with an immediate hypersensitivity reaction after peanut ingestion, positive skin prick test to peanuts, and positive by double-blind placebo-controlled food challenge (DBPCFC). We excluded participants if they had a major chronic illness, if the care provider or a present household member had suspected or diagnosed allergy to peanuts, or if there was an unwillingness or inability to comply with study procedures. Our primary outcome was desensitisation, defined as negative peanut challenge (1400 mg protein in DBPCFC) at 6 months (first phase).
(emphasis mine)-- So the bottom line is that it's unclear (at least from the abstract) whether or not exclusion includes those who dropped out due to side effects of treatment. You know, if participants became "unwilling" via asthma or other allergic reactivity.
The primary outcome, desensitisation, was recorded for 62% (24 of 39 participants; 95% CI 45—78) in the active group and none of the control group after the first phase (0 of 46; 95% CI 0—9; p<0·001). 84% (95% CI 70—93) of the active group tolerated daily ingestion of 800 mg protein (equivalent to roughly five peanuts).
84% is roughly in line with what US researchers have found, too, using similar treatment protocols.
That part is comforting, at least-- it suggests that UK peanut allergy is the same beast as in N. America, and that treatments work the same way there as here.
Same short-term study, though-- six months isn't a long enough follow-up, which is what US researchers have been saying for a year or two now.