Maybe 9th June, which goes on the assumption that BBC4 will be showing the two episodes of Sebastian Bergman on 26th May and 2nd June.
I know it's only a bit of fun, speculating a possible start date. But if that DVD release date is true(and it is a big if) then the 9th would work as well. I was giving the last possible date. To get 6 Saturdays before the hypothetical release date. Or BBC4 could fill the Saturdays with repeats, before starting a new series? They've done this before.