Did the work done by your brother amount to commercial work of done by your brother, but which was absolutely essential to keep the whole thing ticking over? If your brother had not done it, then would it still have to have been done and if so, would that cost be more or less your brother is now wanting?
The reason I ask is because under the Supply of Goods and Services Act or the later Consumer Rights Act 2015, if there is no price agreed for a job to be carried out (forgetting that this is a will/probate/inheritance situation) then the price has to be reasonable. Hence, your brother would only be able to charge the market rate and it would come down to however much that was.
He cannot charge for the odd little bit of helping out or house clearance here and there, only if the work was essential and done on a commercial basis.
Can I clarify anything for you?
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By all means ask your brother to review his bill and if necessary, contest it in court. Hundred pounds per day is not an unreasonable amount but it depends whether he actually did the number of days that he is claiming for and whether he did full days.
The full heading of any letter is ” Without prejudice save as to costs”. However you only need to do that on the letter if it contains anything which could be construed as an offer or admission. Otherwise, it is just open correspondence there is no need for it.
What you might want to do is present him with some hard evidence of the number of days and hours he works and tell him what you are happy to agree with rather than just a blanket non-agreement. It may be that the cost of arguing over the amount you are arguing over, which for solicitors would be £200 per hour or thereabouts, is going to actually cost more than the amount of money being argued over.