The duo were both on the recent 'A tour of Sri Lanka and 20-year-old Cook, who also led the England Under-19 side to the semi-finals of the last junior World Cup, in India, confirmed the promise he'd shown in the sub-continent with an innings of 120.
And while neither he nor Prior are current candidates for the Test team, the Sussex batsman-wicketkeeper boosted his chances of a One-day call by making 70 off 65 balls.
With Owais Shah making 78 on his Middlesex home ground, MCC declared at 275 for two and at stumps Warwickshire were 70 for three in their second innings, a lead of 140 ahead of Monday's final day.
Prior, who opened the innings alongside Cook, was caught at slip by Jonathan Trott following a a late-cut against fellow England batting hopeful Ian Bell's medium-pace.
But Cook did not throw away the chance of a hundred and by the time he was caught behind off seamer Nick Warren he'd struck 15 boundaries in his 245-ball innings.
His dismissal prompted a declaration with Warwickshire changing their batting order to give those players who missed out in the first innings a chance of time in the middle before the start of next week's County Championship.