I don't know about WFH expenses, but I have made 2 types of mileage related claim in the past. Neither is worth giving a claims service a cut of your cash for.
1) You can reclaim income tax paid on the 20p difference between the HMRC approved rate of 45p per mile (see
here) and the miserly MOD official duty rate of 25p per mile for your first 10,000
official duty miles per year (the HMRC rate reduces to match the MOD rate after that, so there is nothing to claim). If you are not required to fill out a self assessment tax return for other reasons (eg rental property, pension tax, income over £100k) then you can apply for 'Mileage Allowance Relief'
here. To get the data needed, you can run a JPA expenses search setting the start and end dates to the tax year in question and adding up the mileages and amounts paid. Any journeys where you ticked "start or end at RWA" will be abated by the distance from your home to duty. (Useful error check: if you have added everything up and abated correctly then your total paid divided by your total mileage will be 25p.) If you
do already fill out a tax return, then multiply your total abated mileage (up to the max of 10,000) by 20p (the amount MOD made you pay yourself) and enter this to the "Allowable business expenses" box. Either way, you need to pay attention to what HMRC does to your tax code as they may assume that you be will entitled to similar relief in the next tax year and attempt to make PAYE work for you, out of the box.. very considerate of them, but it introduces the risk that if you make fewer claimable journeys you'll end up underpaying tax and needing to send the taxman a corrective sum at year's end!
2) If you get an assignment order for less than 2 years then it should meet the conditions of what HMRC terms 'temporary employment'. Now all payments for journeys between your permanent home and place of work become subject to the same tax claim regime, claimed in the same way. So, add up your total mileage driven between home and duty, multiply the first 10,000 miles by 45p and the rest by 25p, deduct the amount of GYH and/or HDT you were paid, and the result is an allowable business expense for your tax return. Note that this only applies if the assignment was only for less than 2 years *from the outset*. I would suggest you keep a copy of your assignment order as evidence. If a 3-year assignment gets shortened to 1.99 years within a week of you starting, then tough luck. Likewise, if your 1.99-year assignment gets extended to 3 years after a week, your tax claim potential evaporates at that point. Note also that you only get one lot of 10,000 miles per year from HMRC, so don't double-count it if claiming both for official duty and temporary assignment reasons. The
HMRC tax manual entries are worth reading (including following sub-links) before you consider making claims under this heading as it is quite complex. (When it talks about workplaces not being temporary if expecting to spend more than 80% of the "employment" there, remember it is written with contractors in mind: military "employment" means until your exit date, so the 80% limit only becomes relevant in your final 2.5 years of service. See
here, where the relevant example is someone going on secondment while remaining on a single contract of employment, so would be entitled to claim for temporary employment, unlike someone who went onto new terms for the 2 year period).
[All offered with the usual disclaimer that this is not professional tax advice, consult an accountant, no liability accepted, etc]