Thanks for your question, I am Sam and I am one of the UK tax experts here on Just Answer.
Yes you are entilted to a mileage allowance as your work requires you to travel all day/every day, and I agree that the first trip out and the last trip home are not to be counted UNLESS you have no permanant workplace to attend in which case ALL travel is allowable - see link here from the 490 booklet and see Page 8 item 2.6 - where it highlights Barry as a tree surgeon who works all over and has no permnant workplace.
You do not advsie whether your employer makes good any of the costs for mileage, but if its less than 45p a mile for the first 10,000 miles (and then 25p amile therafter) then you can claim the difference from HMRC, But any element that your employer pays you should not be taxed if it falls within these limits.
Whether you claim these allowable expenses through P87 expenses claim form or via self assessment they still result in your income being £15000 less allwoable expenses (you indicate £4600) so net income that the HMRC Tax credit office would use is £10400 for tax credit purposes. (Then add back in anything your employer pays you for mileage - as you canno have it twice)
But your thoughts on this are accurate and the tax credit office know nothing about allowable expenses is either employment or self employment and therefore I am surprised they are attempting to tell you whats right and whats not!
I would be inclined to just ring the tax credit line up again and state your income (after allowable expenses) will be £10,400 (ONLY if you are not paid any nileage from your employer, if you are then please advsie what you are paid and I can advsie further)