which matches did he play with that team?
He played against Leicestershire, Surrey, and Essex.
Ian Johnson (cricketer)
Johnson started the tour well, taking 7/42 in an early tour match against Leicestershire, followed by 5/53 against Surrey. Against Essex, Johnson took 6/37 in the second innings. Earlier in the match Australia had scored 721 runs in a single day; Johnson made 9.

was cricketer ian johnson a bowler or a batsman? A slow off-break bowler. when did he make his international debut? In the 1935–36 season . was he a part of any historic team? Yes, Bradman's 'Invincibles".
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Ian Johnson (cricketer) [SEP] Bradman's "Invincibles"
He had more success in the Second Test at Lord's taking three wickets in the first innings as Australia won the match by 409 runs. Johnson failed to take a wicket in a rain-affected Third Test at Old Trafford, and was replaced after the Fourth Test, having taken only seven wickets in the series at an average of 61.00. "Wisden Cricketers' Almanack" noted that while Johnson had started the tour well, he was not as effective in English conditions as Australian. Nonetheless, Johnson played an important role in maintaining the Australian team's unbeaten record, bowling more overs than anyone other than Bill Johnston—allowing Bradman to rest Keith Miller and Ray Lindwall, his fast bowling pair, for the important matches.