A STEP member (Society of Trust and Estate Practitioners) or ACTAPS (Association of Contentious Trusts and Probate) will have particular expertise with dealing with wills and estates. Equally a member of the Probate Section of the Law Society will have greater experience.
Some lawyers just do general practice, some specialise. I would always recommend using a specialist - particularly for something that is likely to end up in Court.
But nothing to stop you using a non specialist practitioner.