123 reg emails going to spam

I have a domain registered with 123-reg with a business website (via Website Builder) emails. I am experiencing a recurring problem with my 123 reg emails going to customers spam boxes. I would like to know how to migrate emails away from 123 reg to another provider without having to redesign my website or change email addresses.

Essentially I need service continuity with email and website but without the 123-reg service. Would welcome the best migration ideas and costs. Sorry, can't set a budget as I have no idea of likely costs/timeframe.

Thanks

Sergi