Barrington's a tricky one - his average of nearly 60 in the 1960s, when only Sobers was at the same level* and the other top batsmen of the decade* (Simpson, Dexter, Graveney, Cowdrey, Lawry) averaged around 50 suggests he should be thought of as an all-time great, and so is underrated.
OTOH, he does tend to get mentioned when people pick their all-time England XI these days, whereas in the late 80s I had the impression that the cricket writers old enough to have watched cricket since the 50s (if not earlier) wouldn't have considered putting him ahead of Hammond, May or Compton, and quite often rated him below Dexter, Cowdrey and (Bill) Edrich - they would probably say that he's now overrated by people who only know his average, and didn't have to watch him taking 7 hours to score 137 against NZ.
From vague memories of reading an article by Barrington, he reckoned he adapted his technique better for overseas pitches than most of his team-mates (his average in away Tests was nearly 70 - Dexter and Cowdrey were still around 50, and May and Graveney were in the 30s), which perhaps made his success less noticeable to the UK cricket watchers of the time.
*To be strictly accurate, Pollock (another ATG) and Walters had similar/better averages in about 20 Tests, but Walters didn't sustain this level and Pollock's career was of course cut short.