"Time" is used in the Norfolk dialect to mean "while" e.g. "I'll cook the breakfast, time you're milking the cows".
This conjunction use does have an entry in the OED. The examples are mostly American, but it is almost certainly English in origin - used as part of the Norfolk dialect today, in exactly this way - to mean "while". It may be in more widespread dialectal use in Britain - it is just that Norfolk is the one with which I am intimately familiar.
C. conj.
- Eng. regional and U.S. regional. During the time that; while; when. Now rare.
1875 E. Tweddell Rhymes Cleveland Dial. 22 Let's be off,..tahme
it's seea nice an' leet.
1926 E. Ferber Show Boat 124 I was keelboatin' time you was
runnin' around, a barefoot on the landin'.
1948 M. Carbery & E. Grey Herts. Heritage 145 Time, when: ‘Time we
lived Redbourne way.’
1950 R. Moore Candlemas Bay 13 Time Joel Walls had his net, one
night he caught seven hogsids.