Can I claim any credit for the council tax paid to the UK on my Canadian tax return?

The only time I can think of you claiming this on a Canadian return would be if you were using the property as a rental or business operation, and were liable for Council tax on the property. The foreign tax credit applies to income tax paid on income from foreign sources. While council taxes in most counties have a means test, where the amount payable can be reduced or eliminated, this does not make it a tax on income, and thus it cannot be applied to reduce Canadian income tax.

Probably not. The Tax treaty would cover that. I'd expect that council tax is like property tax and paid to the local government, not the national one. The credit would be for income tax paid to the crown. And no property tax credit either, the property has to be in the province that would give the credit for it to count for that. For example, the Ontario credit is only for rent or property tax paid on a residence in Ontario.