This month's adviser mag mentions that LAs have 'complete discretion to grant discounts and exemptions beyond those allowed for in the legislation.'

What i wanna know is, has anyone managed to get an extra discount? If so, how did you go about it?

I don't think these "extras" can be applied to individual cases, but may apply to certain specified GROUPS of people. Our own Borough Council disregards income from War Pensions and War Widows Pensions IN FULL.

Is this discretionary housing payments made in respect of council tax? See The Discretionary Financial Assistance Regulations 2001 (SI 2001/1167). Allows payment of up to the full CT liability where a claimant 'requires financial assistance'.

It's not part of CTB or DHPs.

The piece in Adviser refers to S76 of the Local Government Act 2003 which inserts a new section 13A into the Local Government Finance Act 1992:

"13A Billing authority's power to reduce amount of tax payable

(1) Where a person is liable to pay council tax in respect of any chargeable dwelling and any day, the billing authority for the area in which the dwelling is situated may reduce the amount which he is liable to pay as respects the dwelling and the day to such extent as it thinks fit.

(2) The power under subsection (1) above includes power to reduce an amount to nil.

(3) The power under subsection (1) may be exercised in relation to particular cases or by determining a class of case in which liability is to be reduced to an extent provided by the determination."

That seems to me to give the Council the discretion to reduce CT in any way it sees fit, or even to waive the CT altogether.

I can't find anything setting out how this should be done. Presumably Councils should set up some sort of procedure to deal with requests under S13A, but I doubt if most of them have.
A letter to the CT billing section setting out the client's circs and requesting a reduction or waiver would be a starting point. If they have a procxedure set up they can ask you to follow it.
It does appear to be completely discretionary so presumably a refusal to reduce or waive would only be challengeable by judicial review on Wednesbury type grounds. Or it might be possible to raise at a liability order hearing?