When can you start looking to buy a house?

My boyfriend and I are currently saving for a mortgage and I'm just wondering when is best to start looking around? I think the sooner the better but I've heard/read it's best to wait until you have your full deposit then if you want to put in an offer there's no waiting further. Also because we are still saving is there someone we can seek advice from like a mortgage broker, is that the correct term? Plus there's the solicitors fees but I don't believe you need a solicitor while your still just looking and not yet got your deposit.
I'd appreciate any helpful advice, thanks:)

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