If you refuse consent the IVA might not go ahead, but that might lead to bankruptcy, in which case the house will be at risk.
There are ways which CF could, if they desire, work around the issue .... they could simply ask creditors to accept an extension to the IVA instead ( which would be the likely outcome anyway ) or they could follow the regulatory bodies new Covid-19 guidelines, whicg also offer an 'out' ... have a read here, towards the end of the article: https://debtcamel.co.uk/coronavirus-new-rules-ivas/
They should be following this anyway: The changes are not discretionary.
If you consent, at the end, you will be joined in the new lending as a co-owner, but you could get a solicitor to cover this in an agreement regarding any future equity split when the house is eventually sold when your marital assets are split. Currently, I am told, less than 1% of IVAs actually manage to remortgage or get secured lending at the end and, I imagine, this figure will drop further in the coming post - covid financial mess.