You would be able to claim relief on the FULL cost of laundry and dry cleaning services.
An officer has a standard tax relief of £367 pa (well it was) which is deducted from his gross pay (her allowance is greater, about £418 iirc). In UK this is expected to cover laundry, dry cleaning, replacement etc. All for £92 per year.
If you are overseas and drawing LOA the additional costs should be factored in to LOA. However if you are on rates, and the you have additional laundry costs for both civilian and uniform clothing, you should be able to claim an element towards their maintenance. Be realistic and prepared to argue your case if the tax man challenges you.
On realism, how often do you have a suit or uniform dry cleaned? My work trousers were machine washable!