You'll be on SH for about 6 years currently before having the seniority to get onto LH. With the current SH review and focus on competing better with the like of easyjet Ts and Cs will drop further and time to LH may increase. That said it's still a great place to be In my opinion.
I can only echo the part I underlined... It's sometime worrying hearing current BA pilots implying the goal posts have moved, and when they joined they were told "X years to Command, Y years to LH" and it did not happen
Moves to LH and/or LHS are essentially seniority and retirement driven. When you have some SH Capts bidding to RHS LH already, I leave the applicant to judge what effect the 2-3 "agreement" "business" reviews currently going on might have
(1 clue is that "SH" appears in 2 of the savings / review items)