[1] https://assets.publishing.service.gov.uk/government/uploads/...
Sourced from gov.uk [0] (ods spreadsheet file), pedestrian fatalities, in 2016, are 7.1 per million population in the United Kingdom; 470 pedestrians killed, and 18.5 in the USA; 5,987 pedestrians killed, confirmed for USA by NHTSA[1].
For overall road traffic deaths, in 2015 UK 2.9 per 100k population (1,770 total deaths) 22.9% pedestrians, USA 10.6 per 100k (32,719 total deaths, approx 5x the UK population, 18x the total reported deaths) 14.1% pedestrians, source WHO, table A2 [2].
Every international comparison and US source I found prefers per 100k or million population and agrees with the above. I stopped there, so can't compare the gov.uk doc you linked, or why the US data in BMJ differs so markedly.
[0] https://www.gov.uk/government/statistical-data-sets/ras52-in... (Download RAS52001)
[1] https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/... (PDF. Note they report per 100,000 not million, so it's 1.85)
[2] http://www.who.int/violence_injury_prevention/road_safety_st...
Have I got this right?
In the UK it appears they're counting the deaths per billion miles that people walk.
In your BMJ article it appears they're counting deaths per billion miles that people drive.
Pedestrian deaths per billion miles that people drive seems an odd choice of measure.