There is an interesting twich here. In the late 30` ies, Polands military had some military training camps for jewish activists in Poland, for example officers from the Irgun groupe in Palestina.
The background: Poland wanted to encourage jews to emigrate from Poland, and if they wanted to emigrate to Palestine, so be it. And thus, they did helped the Irgun and in some degree the Haganah with training (including sabotage technique for Irgun), military leadership, weaponlore, weapons and money to buy more weapons locally. They also helped with the selve illegal transportation into Palestine...
That is why the Irgun members in Palestine, whom happily did sabotage on british military vehicles, warned and adviced the poles to paint polish marks on their british vehicles... To not get them sabotaged. As a little Tx for old favors.
Btw, The british could and did organize a full jewish brigade (and could probably organize more if they wanted to). I suppose many of these soldiers there were the ex-polish soldiers mentioned, whom leaved the Anders army, + probably some of the Irgun and Haganah mentioned, whom joined the british army to fight actively against the nazis.
For the british it was a good source: trained soldiers, whom are eager to fight against the enemy, you dont just find on the street every day!