DH saysd (his mum told him ) that when they flower they are going to seed so you must harvest, no point in leaving them any longer.
I have been looking on the I'Net and it says that flowering just means that new little tubers are getting started, so really, you should harvest sometime (like a long time) after flowering, to let the little tubers become decent size actual potatoes.
Bob Flowerdew was going on about spuds on Gardener's questiontime.
He said - you can harvest once you see flowers - no point before that. But also if you pick the flowers off you can increase the yield.
You can harvest any time from now onwards, right through until October (depending on whether they are first or second earlies, or maincrop). The longer you leave them the more prone they are to slug damage.
Also what out for blight from now on - if you see it you need to remove all the green stems, leave for a week and then harvest - and get rid of anything that has brown marks on it (and not in the compost bin).
Do you know what type of spuds they are ?
In this case MIL is not quite correct (but don't tell her I said that )