I think you are lumbered with the Pension Service assessment. HB Reg 23(1) says:
“the relevant authority shall … use the calculation or estimate of the claimant’s … capital made by the Secretary of State”.
Reg 23(7) & (8) allows you to substitute your own calculation of capital where “subsequent to the [AIF assessment] the claimant’s capital rises to more than 16,000…”
I think this means that there must be a change in the amount of the claimant’s capital from less than 16,000 to more than 16,000. It does not allow the council to override the AIF at a time when the Pension Servcie considers the capital to be less than 16,000. This rule exists purely because of the AIP rules in Pension Credit, which would delay the effect of such a change for several years. There is absolutely no scope for the Council to take a different view from the Pension Service at the outset.