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I'd speak to the mortgage advisor before 1 so you have a solid idea of your budget, permutations, etc. Using a free one is fine if your circumstances are straightforward (e.g. PAYE, standard property, etc)
Solicitor is going to be at the same time as 2. When you accept an offer the legal stuff on the sale starts. I'd have someone lined up at that point so it's ready to go.
Also, just in case you're not planning to, I'd start viewing properties ASAP. That can inform you on what price you need, whether the mortgage is feasible, etc
I'll PM you details of the solicitor I used (someone else on here recommended him and he's been good). I wouldn't worry about location, I've never met my solicitor and the mortgage advisor I met for some preliminary chats and then all the coronavirus stuff kicked off and it was all over the phone anyway.
Also, at what point(s) in the process do you usually instruct/engage either a mortgage advisor and/or a solicitor.
My guess is between 3 & 4?