When I was researching the Indomitables tour I came across two RL cricketers. I always thought RU had cornered the market with Wilf Wooller who captained Glamorgan, and captained the Wales RU side.
Willie Horne that supreme half back from Barrow was on the Lancashire ground staff, but a tour to Australia starting in April to september is a killer for a future cricketer. The most exciting one was Ray Lindwall, who was full back for St John Illawara, he didn't play against the Indomitables as they only played against regional teams , and because he had played for the national side against New Zealand at cricket he was lined up for an international cricket career.
I bet the English batsmen in 1948 wish he had stuck to rugby.
I saw Lindwall at Park Avenue in '48 and his run in and delivery were poetry in motion. Incidently the match came closest of all games of the tour for the Aussies to lose. It was rain affected, but the major disappointment was Bradman the captain resting himself and Lindsay Hassett deputizing for him.
Certainly since the war these have been the only cricketers I have found,any more would be welcomed.

Don't know if he played at all, but wasn't legendary Aussie batsman Victor Trumper involved in establishing RL over there?

In the 70's, one of Eddie Waring's annoying tics was invariably to refer to Leeds forward Phil Cookson's cricketing exploits. To the best of my knowledge, he can't have been more than a local league player at most.

more recently, Liam Botham played cricket, RU and RL professionally.

Arthur Clues was a very good grade cricketer in Australia.

Mike Smith played for England at Cricket and RU.

I remember Matt Adamson celebrating a Leeds try with a perfect seam bowler's action!

My mate wrote to the League Express to argue that summer rugby would be scandalous as it would prevent the likes of Deryck Fox from playing cricket. It failed to sway Maurice and co.

Mentioning ArthurClues, he was very prominent in the '46 tour, and at that time was a serving policeman. Very big friends with his arch rival on that tour, namely Frank Whitcombe they had many stormy matches against each other in the tests. Nothing was mentioned about his cricket abilities though.
Ray Lindwall was terrifying on the '48 tour, and when he played at Park Avenue he bowled from the football end, actually starting his run up by the rails. Keith Miller was his bowling partner in that match. Len Hutton was the only English batsman able to play their bowling with confidence. Surprisingly the selectors dropped him from the fourth test. One of the most surprising non selections ever. Good job they brought him back for the last test as in the first innings he batted through the innings as all the rest of the side capitulated.