In their final home match of the season, Warwickshire chose to bowl and were unlucky not to take more than one wicket in the morning session.
Olly Hannon-Dalby, in particular, maintained high pressure, conceding just three runs from his first seven overs, but the ball frequently beat the bat rather than taking the edge.
Elgar and Paul Walter added 41 in 14 overs before the latter was lured into driving at a wide ball from Nathan Gilchrist and edged to wicketkeeper Alex Davies.
Elgar moved diligently to 48 in 144 minutes then perished in similar fashion to his opening partner. The left-hander edged Gilchrist to Rob Yates at second slip.
When Westley drove around an Ethan Bamber yorker, Essex were 111-3 but Allison and Critchley ensured there was no collapse with a measured partnership of 98 in 25 overs.
Critchley was closing in on his 33rd first-class half-century when he nicked an excellent ball from Michael Booth to Davies.
Allison found another resolute partner in Pepper. Both scored Championship centuries against Warwickshire at Chelmsford in July and this time they added 77 in 20 overs.
Allison, having spent quite some time in the 90s, then attacked the wrong ball from Bamber as Yates accepted his 16th Championship catch of the season.
That proved to be the only wicket with the new ball. Again, Warwickshire’s seamers bowled well without much luck but Pepper completed his half-century in the day’s penultimate over and Essex can be satisfied with a strong day’s work by their batters.
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