Transfer of ownership following in-laws death

Short version, my in-laws passed away 3 years go, leaving behind their house and a flat they rented out. House worth ~ £180K and the flat ~ £120K, and various other financial assets. My wife wants to take ownership of the house and her brother the flat, and she gives him £30K to account for the difference in value. The house is currently registered in their late fathers name, and the flat in both my wife and her brothers name. He is perfectly happy with that arrangement, and is acting as executor of the will anyway.

I've tried to find the answer on the Land Registry site, but am getting more muddled the more I look. Can anyone advise me as to the most efficient way to transfer the ownership of the house from the estate to her? It seems to suggest this might be achievable without involving a conveyancer, but I can't identify the fee required or the exact process. The process of taking my wife off the flat is technically his problem, but as there's no disagreement about this between them, I'd be interested in that process too to help him out.

   Many thanks for any suggestions/advice.

Nicholas - you'll need probate for the Father and then the executor(s) can transfer the ownership to your wife as a beneficiary - HMLR Guide Page  · HM Land Registry
The registration fee is payable under Scale 2 on the current market value of the house
As to the flat your wife and her brother can transfer the ownership from their joint names to just his - Registering land or property with HM Land Registry: Change the registered owner name - GOV.UK
Whilst the ownership is 'his problem' your wife will still need to be involved to achieve the end result wanted

Land registration is complex, designed to protect legal and financial interests in property. There can be significant consequences for any error. Please consider seeking legal representation. Before making an application without legal representation, it is important to consider the benefits of using a conveyancer.