Where do I find a financial advisor specialised for high net worth clients?

dunstonh

IFAs typically charge 1% p.a. to look after investments, 

No they don't.   The dominant figure is 0.50%.  Smaller amounts tend to be at 1% but then tier down with larger amounts.  Greedy wealth managers charge 1% (plus DFM fee often) with no tiering.

there would be a fairly large initial fee.

Not necessarily.  It is considered best practice to have a decency cap.  Plus, ,many IFA firms have a cap and collar on their initial charge to ensure it remains decent.   The wealth managers tend to be lacking in the decency cap though (until you tell them that an IFA can do it cheaper and miraculously they then lower their charge)

I’ve searched unbiased and locally I can only find the names of small firms and random individuals.

unbiased is not the best way nowadays. it used to be an IFA directory but nowadays it includes FAs and is more a of lead generation site.  Most of the IFA firms I know no longer pay to have a proper listing on unbiased any more.  

Most IFAs firms are small local firms of 1-5 advisers.   Just as it used to be with solicitors and accountants.

 I think I would feel more reassured with a somewhat reputable name I’ve heard of e.g does the likes of Coutts etc offer this kind of service?

We took some business off them earlier in the year and the client saved a fortune by doing so.   Plus, the person told me that they hadn't had personal meetings with them as contact was over the phone.  It was nearly always a different person each time.    That is generally what happens when you see the nationals.      The nationals make a good training ground for new advisers who then tend to leave to become IFAs once they build confidence and experience