[4] Allinson performed extensively on Broadway, where he took over the role of Professor Henry Higgins in My Fair Lady during the 1960 season opposite Pamela Charles as Eliza Doolittle, having toured as standby for Rex Harrison.

On Broadway he also created the role of "Warnie" in the original production of Shadowlands, starring Nigel Hawthorne and Jane Alexander.

He appeared as Hobson in the short lived musical Arthur, based on the Dudley Moore film of the same name.

He appeared on Broadway productions in, among other shows, An Ideal Husband, Oliver!, Angel Street, Coco, Sleuth, and Hostile Witness.

[6] Allinson understudied both Rex Harrison and George Rose in the production of Kingfisher and did a one-man show, "Meet George Orwell," that he performed at the John Kennedy Presidential Library Theatre in Boston and Trinity College, Oxford, among other venues, in the 1990s.