Plumbing question.

I’ve noticed that when my washing machine drains water backs up all over the utility room (it’s a brand new machine – I replaced the old one as it did the same thing). At the same time the kitchen sink clogs indicating to me the pipes are connected.

I’ve got a plumber coming on Thursday- I assume this isnt a straightforward Mr Muscle Unclogging gel situation and there’s a blockage on the washing machine pipe side that they’ll need to sort? Just trying to make sure I don’t get scammed with a massive bill