Just some general thoughts of mine - note others may take a different viewpoint here !
Vehicle as I don't keep a mileage log and previous inspection both allowed a 50% personal use so never need to. Will do after this but then who in HMRC is going to sit down and actually check all the mileage covered
Unfortunately i would say the onus is 100% on you to fully substantiate all claims made - if you have got away with an agreed 50% split before that doesn't mean anything really.
Note any evidence you can give in this regard should be looked at by the tax inspector so you should be able to justify your claim by providing some samples / estimate details of normal journies or something similar to justify your claim. If your claim is reasonable a simple log for the next 2-3 months may suffice if this is fair and reasonable (Ie you don't suddenly stop using personally or use a peak travelling season work wise - that can work both ways if you drive down to france on personal one off annual trip that may prejudice the figures against you.
Use of home for office and storage. His figures for what he thinks is allowable are so low I have to wonder whether HMRC actually know the value of a lot of things such as the cost of office space and rental of storage space never mind the pain of having every time to go there to work. Far easier to work from home using one room and a storage building.
Yes i would say sometimes hmrc in this regard will come up with nonsensical figures - but it''s equally likely they could screw you down on the detail if what you say gives them the ammunition they need to - some expert advise here may help you. Note your logic is a bit out of kilter here - you can't claim just because you would have spent similar elsewhere - the facts are that if there minimal additional actual costs then really you aren't paying owt extra, thankfully hmrc are normally reasonably fair when fair proportionate calcs are used - although that may not be the case here. I would say in this regard though if the facts are as per previous visit and hmrc accepted those calcs as being reasonable back then i would not expect them to question them now without the inspector being able say why - eg more recent guidance issued that make previous calcs obviously out of synch with what you could expect to claim.
You always have the option to ask another inspector to look at things if you reach impasse you want to leave this option as late as possible though if you can still get the current bod to see reason to some degree.
It may be worth running everything past an expert too just to see if it is the way you are presenting your case that is not really working with hmrc.