If the Will appoints an executor (who is not a family member and is, say, a solicitor) the family members cannot ignore the Will. They can ask the solicitor to "renounce" (which is to disclaim) his appointment as executor but he does not have to do so.
They find out the total of the estate by firstly doing a paperwork search in the property. They then write to all asset holders they have identified and also obtain bank statements (which are often a good source of information about other assets/accounts). Once they have the figures back from the asset holders, they can they apply for Probate.
The only relevance of "lifetime gifts" are in the 7 years prior to death. These will only be relevant for inheritance tax purposes if the estate (including the gifts) is over the IHT threshold. However, at £100k, unless the deceased has made over £200k of lifetime gifts in the previous 7 years this is unlikely to be relevant. A solicitor does not have access to any information a non-professional executor wouldn't have. He probably just has slightly more knowledge about where to look.
Personally, on an estate of £100k, I wouldn't bother with a solicitor and just appoint the family members as executors. They can then choose whether to do it themselves or ask for help.